Projectile Motion Help: Solving Two Problems with Specific Numbers

[ArthurYan]

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.

 

[LowlyPion]

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?

 

[nlightner]

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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