Kinematics Problem: Time to Reach Maximum Height with Initial Velocity 30m/s

In summary, the ball is thrown vertically upward from the ground with an initial velocity of 30 m/s and an acceleration due to gravity of 10 m/s2. It reaches its highest point in 3 seconds and at this point, its velocity is 0 m/s. The height it reaches is 45 meters. On its way up, at a distance of 33.75 meters, the speed of the ball is equal to half its speed of projection.
  • #1
tommy2st
15
0

Homework Statement



A ball is thrown vertically upward from the ground with an initial velocity of 30 m/s. Assume the acceleration due to gravity is g = 10 m s-2.

How long will it take for the ball to rise to the highest point on its trajectory? (AF:no decimals)


i got v1 = 30m/s
a= 10m/s2
x1=0

but i can't think of where to start given this information can someone point me in the right direction

Homework Equations





The Attempt at a Solution

 
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  • #2
What will be the velocity of the ball when it reaches the highest point of its trajectory?
 
  • #3
0 is the final velocity. is the answer 3s? i think i may have got it

30=10t
t=3

anyone am i right?

also the height it reaches using 3?

would i use d=30*3 + 1/2(10)(3^2)
 
Last edited:
  • #4
anyone?
 
  • #5
tommy2st said:
0 is the final velocity. is the answer 3s? i think i may have got it

30=10t
t=3

anyone am i right?
Right!

also the height it reaches using 3?

would i use d=30*3 + 1/2(10)(3^2)
Almost. Careful with signs.
 
  • #6
would it be d= 30*3 + 1/2(-10)(3^2)?

giving me 45?
 
  • #7
tommy2st said:
would it be d= 30*3 + 1/2(-10)(3^2)?

giving me 45?
Yep!

You can also solve it using the concept of average speed. What's the average speed of the ball as it rises?
 
  • #8
average speed 15 m/s?

also i need help with this part... On the way up, at what height is the speed of the ball equal to half its speed of projection?

i get that it wants me to find at what distance v = 15 but I am having trouble munipulating the equations to solve this
 
  • #9
tommy2st said:
average speed 15 m/s?
Right. So you can find the distance using average speed X time.

also i need help with this part... On the way up, at what height is the speed of the ball equal to half its speed of projection?

i get that it wants me to find at what distance v = 15 but I am having trouble munipulating the equations to solve this
Solve it exactly as you solved the first part. First figure out the time.
 
  • #10
okay thank you ill try and edit this

t=1.5

d=(15)(1.5)+(1/2)(-10)(1.5^2)= 11.25?

or (30)(1.5)+(1/2)(-10)(1.5^2)= 33.75?

i think its the second one
 
Last edited:
  • #11
tommy2st said:
okay thank you ill try and edit this

t=1.5

d=(15)(1.5)+(1/2)(-10)(1.5^2)= 11.25?

or (30)(1.5)+(1/2)(-10)(1.5^2)= 33.75?

i think its the second one
Right. The initial velocity is 30 m/s, not 15. (That's the final velocity.)

Verify your answer using the average velocity method.
 
  • #12
thank you so much for your help doc!
 

1. What is Kinematics?

Kinematics is a branch of physics that studies the motion of objects, including their position, velocity, and acceleration, without considering the forces causing the motion.

2. How is Kinematics used in real life?

Kinematics is used in various fields, such as engineering, robotics, and sports, to analyze and predict the motion of objects. It is also used in the development of transportation systems, such as cars and airplanes.

3. What are the three main equations used in Kinematics?

The three main equations used in Kinematics are the equations of motion: v = u + at, s = ut + 1/2at^2, and v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, t is the time, and s is the displacement.

4. What is the difference between linear and angular Kinematics?

Linear Kinematics deals with the motion of objects in a straight line, while angular Kinematics deals with the motion of objects in a circular or rotational path. Angular Kinematics also involves concepts such as angular velocity, angular displacement, and angular acceleration.

5. How do I solve a Kinematics problem?

To solve a Kinematics problem, you need to identify the known and unknown quantities, choose the appropriate equation, and substitute the values into the equation. It is important to use consistent units and pay attention to the direction of motion. You can also use graphs or diagrams to help visualize the problem.

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