Projectile Motion Help: Solving Two Problems with Specific Numbers

In summary, there are two problems that need help. The first one involves showing that a dart, aimed directly at a falling target, will always strike the target, using a specific set of numbers. The second problem involves finding the time the ball is airborne, the horizontal distance from the glove to the edge of the roof, and the velocity of the ball just before it lands in the glove. The given angle is 33 degrees above the horizontal, and the ball drops 5.2m before being caught. The equations that may be useful are X = (vi^2sin2FETA)/g and T = ((2vi)sinFETA)/g. The attempt at a solution involved using SOH to find the change in
  • #1
ArthurYan
2
0
I have two problems that I need help on.

Homework Statement


For the circus, they show a demonstration of projectile motion that usually warrants applause from the audience. At the instant a dart is launched at a high velocity, a target (often a cardboard money) drops from a suspended position downrange from the launching device. Show that if the dart is aimed directly at the target, it will always strike the falling target. (Use a specific set of numbers). So yeah, you're not given anything.

Homework Equations


No idea what equations you need.

The Attempt at a Solution


No idea on what to do.

Homework Statement


A child throws a ball onto the roof of a house, then catches it with a baseball glove 1 m above the grown. The ball leaves the roof with a speed of 3.2 m/s.
a) For how long is the ball airborne after leaving the roof?
b) What is the horizontal distance from the glove to the edge of the roof?
c) What is the velocity of the ball just before it lands in the glove.

Two details that weren't given to you is that the angle is 33 above the horizontal. However, because the ball is rolling DOWN on the roof, the angle, and the whole diagram is flipped around. Also, as the ball leaves the roof, it drops 5.2 m before it is caught.

Homework Equations


These equations may be of use:
X = (vi^2sin2FETA)/g
T = ((2vi)sinFETA)/g

The Attempt at a Solution


What I did is that I used SOH to find DELTA Y, then I subbed in everything to DELTA Y = (viy)(DELTA T) - 1/2gDELTA T^2. Then I used the quadratic formula to find T, but I kept getting a math error.

ANY HELP WILL BE GREATLY APPRECIATED.
 
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  • #2
For the Circus, aren't the bullet and the target both dropping with the same acceleration? Then doesn't that mean that the horizontal velocity, so long as it is fast enough to get there before the ground interrupts the act, will continuously close the distance until impact. (If you were in the frame of reference of the object all you would see is the bullet coming straight at you.)

For 2) what is the component of vertical velocity?

Why don't you fill in your equation with the numbers you used?
 
  • #3


Hello,

I can provide you with some guidance on how to approach these two problems.

For the first problem, we can use the equations of projectile motion to solve it. The key here is to break down the problem into smaller parts and then use the equations to solve for the unknowns.

First, let's consider the motion of the dart. We know that it is launched with a high velocity and that it will follow a parabolic path due to the force of gravity. The target, on the other hand, is simply falling down due to gravity.

Since the target is falling at the same rate as the dart, we can assume that they will both reach the same height at the same time. Therefore, we can set up an equation for the height of the dart and the target at any given time t:

hd = h0 + v0t - 1/2gt^2 (for the dart)
ht = h0 - 1/2gt^2 (for the target)

Where hd and ht are the heights of the dart and target respectively, h0 is the initial height (since both are initially suspended), v0 is the initial velocity of the dart, and g is the acceleration due to gravity.

Now, since we want the dart to hit the target, we can set hd = ht and solve for t:

h0 + v0t - 1/2gt^2 = h0 - 1/2gt^2
v0t = 0
t = 0

This means that the dart will hit the target at the exact same time that the target falls down. Therefore, if the dart is aimed directly at the target, it will always hit it.

To solve for specific numbers, we can assume that the initial velocity of the dart is 20 m/s and the initial height of both the dart and the target is 10 m. Using these values, we can solve for the time t:

10 + 20t - 1/2(9.8)t^2 = 10 - 1/2(9.8)t^2
20t = 0
t = 0

This means that the dart will hit the target at t = 0 seconds, which is when the target falls down.

For the second problem, we can use the equations you provided to solve it. First, let's draw a diagram to visualize the situation:

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Related to Projectile Motion Help: Solving Two Problems with Specific Numbers

1. What is projectile motion?

Projectile motion is the movement of an object through the air, under the influence of gravity. It is a type of motion where an object moves along a curved path instead of a straight line due to the vertical force of gravity acting on it.

2. What are the key factors that affect projectile motion?

The key factors that affect projectile motion are initial velocity, angle of projection, air resistance, and gravitational force. These factors determine the shape and distance of the projectile's path.

3. How do you calculate the range of a projectile?

The range of a projectile can be calculated using the formula R = (v2sin2θ)/g, where R is the range, v is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity.

4. What is the difference between horizontal and vertical projectile motion?

Horizontal projectile motion is when an object is projected horizontally with no initial vertical velocity, while vertical projectile motion is when an object is projected at an angle with an initial vertical velocity. In horizontal motion, the object experiences constant horizontal velocity and no acceleration, while in vertical motion, the object experiences both horizontal and vertical acceleration.

5. How does air resistance affect projectile motion?

Air resistance can affect projectile motion by slowing down the object's velocity and changing the shape of its path. This is because air resistance acts in the opposite direction of the object's motion and increases as the object's velocity increases.

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