Basic Physics Question

When does it reach the maximum...?Think about it... when does the projectile reach its maximum height?Solve for t when v=0.Then substitute that value into the equation x = x0 + v0 t. That will give you the displacement in the x direction when the projectile is at its maximum height.In summary, the projectile is displaced 40 m horizontally and 53 m vertically above its launch point after 2 seconds. The horizontal velocity component is constant, but not 40 m/s, and the vertical velocity component accelerates at 9.8 m/s^2 downward due to gravity. To find the horizontal and vertical components of the initial velocity, equations are used to
  • #1
kara
54
0
2 seconds after being projected from ground level, a projectile is displaced
40 m horizontally and 53 m vertically above its launch point. What are the horizontal and vertical components of the initial velocity of the projectile? At the instant the projective ahieves maximum height above ground level, how far is it displaced horizontally from the launch point?

Any suggestions for that questions, I've already drawn a diagram.
 
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  • #2
Start by writing equations that describe the horizontal and vertical displacement as a function of time.
 
  • #3
so would saying the following make any sense:

the horizontal velocity is constant so the projectile is moving 40m/s right
the vertical velocity changes 9.80 m/s downward because of gravity
 
  • #4
kara said:
the horizontal velocity is constant so the projectile is moving 40m/s right
The horizontal velocity component is constant, but it's not 40 m/s.
the vertical velocity changes 9.80 m/s downward because of gravity
The vertical velocity component accelerates (due to gravity) at 9.8 m/s^2 downward; acceleration is the rate of change of velocity (m/s per s).
 
  • #5
how do i find the horizontal velocity component?
 
  • #6
Use the basic definition of velocity.
 
  • #7
can i do this:

y = 1/2 * g* t^2
y = 1/2 (9.8) (2)^2
y = 19.6
 
  • #8
or is that only when an object is thrown directly upwards and falls directly downwards.
 
  • #9
alright, i know that v = d/t so i'd get v = 40m/2sec = 20 m/sec but do i use the horizontal distance or vertical distance ? and what does velocity give me? is that the horizontal component?
 
  • #10
Well... 40m is the horizontal distance... so that must be the horizontal component of velocity.
 
  • #11
now how do i find vertical component?
 
  • #12
Do what I suggested in post #2. What equation describes the vertical motion?
 
  • #13
y = y0 + v0y*t - 1/2*g*t^2 ?
 
  • #14
so:

- initial position (y0) would be 0 m
- initial velocity (v0) would be 0 m/s
- time would be 2.0 sec
- force of gravity 9.8 m/s^2

so my answer would be -19.6 m/s??
 
  • #15
wait.. wouldn't gravity be -9.8 m/s^2 so that the answer would be 19.6 ?

and i don't know what units it'd be
 
  • #16
what makes you think its initial velocity is 0
 
  • #17
its on the ground?
 
  • #18
The velocity you calculated is if you dropped it off a cliff (in which case its initial velocity would be zero). However, in this case it is projected upwards meaning it was given some initial velocity
 
  • #19
kara said:
so:

- initial position (y0) would be 0 m
OK.
- initial velocity (v0) would be 0 m/s
v0 is what you are trying to find! Don't assume it's anything--certainly not zero. You know it moved up so v0 can't be zero!

- time would be 2.0 sec
OK
- force of gravity 9.8 m/s^2
The acceleration due to gravity is -9.8 m/s^2.

You left out one piece of data: the vertical displacement at time t.

Solve for v0.
 
  • #20
Doc Al said:
OK.

v0 is what you are trying to find! Don't assume it's anything--certainly not zero. You know it moved up so v0 can't be zero!


OK

The acceleration due to gravity is -9.8 m/s^2.

You left out one piece of data: the vertical displacement at time t.

Solve for v0.


take into consideration his equation has a built in negative so if he put g in as negative it would make the object fly upwards
 
  • #21
BishopUser said:
take into consideration his equation has a built in negative so if he put g in as negative it would make the object fly upwards
Right... don't put g as negative! g is always a positive number; the acceleration due to gravity is -g. (Which is why your equation has the minus sign already.)
 
  • #22
so all the - demonstrates is the negative direction?
 
  • #23
you said i left out the vertical displacement at time, so that would be y in the case of this equation y = y0 + v0y*t - 1/2*g*t^2 , and y is 53 m ?
 
  • #24
kara said:
so all the - demonstrates is the negative direction?
Sure, but that makes a lot of difference. The generic kinematic formula (for constant acceleration) is:
y = y0 + v0t + 1/2at^2

When the acceleration is due to gravity (like this problem) we put a = -g:
y = y0 + v0t -1/2gt^2
 
  • #25
kara said:
you said i left out the vertical displacement at time, so that would be y in the case of this equation y = y0 + v0y*t - 1/2*g*t^2 , and y is 53 m ?
Exactly...
 
  • #26
you said i left out the vertical displacement at time, so that would be y in the case of this equation y = y0 + v0y*t - 1/2*g*t^2 , and y is 53 m ?
 
  • #27
alright so solving that equation would give me v0. Now what do i do with that? would i also need to solve for v0 in equation x=x0 + v0t?
 
  • #28
:O I just figured something out... Don't know if I am on the right track but let me know:

If i solve for v0 in equation x=x0 + v0t, then i can sub that into the other equation?
 
  • #29
Solving that equation gives you the vertical component of the initial velocity; you already solved for the horizontal component.
 
  • #30
Alright, so i got 36.3 m/s for v0
 
  • #31
So the horizontal component of my initial velocity is 20 m/s, and the vertical component of initial velocity is 36.6 m/s
 
  • #32
Now i have to calculate how far is its displacement horizontally from launch pt, at the instant it achieves max height.

So i know that its v will be 0 m/s at max heigh.
 
  • #33
kara said:
So i know that its v will be 0 m/s at max heigh.
Right... the vertical component of the velocity will be zero.
 
  • #34
and b/c I am looking for how far its been displaced horizontally from the launch pt. i am looking for x?
 
  • #35
so i can solve for t in the y=y0 + v0-1/2gt^2 equation and sub t into x=x0 +v0t equation and solve for x
 
<h2>1. What is the difference between velocity and speed?</h2><p>Velocity and speed are often used interchangeably, but they have different meanings in physics. Speed is a measure of how fast an object is moving, while velocity is the speed of an object in a specific direction. This means that an object can have a high speed but low velocity if it is moving in a circular path, for example.</p><h2>2. What is the difference between mass and weight?</h2><p>Mass and weight are two different properties of an object. Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. This means that an object's mass will remain the same regardless of its location, but its weight will change depending on the strength of gravity in that location.</p><h2>3. What is the difference between potential and kinetic energy?</h2><p>Potential energy is the energy an object has due to its position or state, while kinetic energy is the energy an object has due to its motion. For example, a ball sitting at the top of a hill has potential energy because of its position, but as it rolls down the hill, that potential energy is converted into kinetic energy.</p><h2>4. What is the difference between force and pressure?</h2><p>Force and pressure are related, but they are not the same thing. Force is a push or pull on an object, while pressure is the force applied per unit area. This means that the same amount of force can have different effects depending on the surface area over which it is applied.</p><h2>5. What is the difference between work and power?</h2><p>Work and power are both measures of energy, but they have different definitions. Work is the amount of energy transferred when a force is applied to an object and causes it to move a certain distance. Power, on the other hand, is the rate at which work is done or the amount of work done per unit of time.</p>

1. What is the difference between velocity and speed?

Velocity and speed are often used interchangeably, but they have different meanings in physics. Speed is a measure of how fast an object is moving, while velocity is the speed of an object in a specific direction. This means that an object can have a high speed but low velocity if it is moving in a circular path, for example.

2. What is the difference between mass and weight?

Mass and weight are two different properties of an object. Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. This means that an object's mass will remain the same regardless of its location, but its weight will change depending on the strength of gravity in that location.

3. What is the difference between potential and kinetic energy?

Potential energy is the energy an object has due to its position or state, while kinetic energy is the energy an object has due to its motion. For example, a ball sitting at the top of a hill has potential energy because of its position, but as it rolls down the hill, that potential energy is converted into kinetic energy.

4. What is the difference between force and pressure?

Force and pressure are related, but they are not the same thing. Force is a push or pull on an object, while pressure is the force applied per unit area. This means that the same amount of force can have different effects depending on the surface area over which it is applied.

5. What is the difference between work and power?

Work and power are both measures of energy, but they have different definitions. Work is the amount of energy transferred when a force is applied to an object and causes it to move a certain distance. Power, on the other hand, is the rate at which work is done or the amount of work done per unit of time.

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