Calculating Vertical Ball Collision Speed at 100m Cliff | Physics Question

[Stroodle]

A girl at the bottom of a $$100\ m$$ high cliff throws a tennis ball vertically upwards. A boy at the very top of the cliff drops a golf ball so that it hits the tennis ball while both balls are still in the air. The acceleration of both balls can be assumed to be $$10ms^{-2}$$ downwards.

With what speed is the tennis ball thrown so that the golf ball strikes it at the top of its path?

I don't know where to start with this one. Is the question missing something? I assume that both balls were both released at the same time...

Any help would be great.

Thanks

 

[ralilu]

for the tennis ball: v = vi + at
0 = vi -10t
(1) write an equation with t = ...

for the golf ball: d=vi x t + (at^2)/2
vi = 0 (for the golf ball) a = 10 and substitute the t from equation (1)

you'll end up with (2) d = ...

for the tennis ball: 100 - d = vi x t + (at^2)/2
a = -10, substite equation (2) for d, and substitute (1) for t

gudluck and tell me waht the answer is

 

[tomcue]

Hello,

Thank you for your question. This is an interesting scenario and requires some calculations to determine the answer.

First, we need to determine the time it takes for the tennis ball to reach the top of the cliff. We can use the equation d = v_i*t + 1/2*a*t^2, where d is the distance (100m), v_i is the initial velocity (which we are trying to find), a is the acceleration (-10m/s^2), and t is the time.

Plugging in these values, we get 100m = v_i*t - 5t^2. We can rearrange this equation to solve for t as t = (v_i +/- sqrt(v_i^2 - 4(-5)(100)))/-10.

Since the tennis ball is thrown vertically upwards, we can assume that its final velocity at the top of the cliff is 0. Therefore, we can use this information to solve for v_i.

At the top of the cliff, the tennis ball and golf ball will have the same velocity, since they collide. This means that the velocity of the golf ball will also be 0 at this point.

Using the equation v_f = v_i + at, we can determine the initial velocity of the golf ball as 10m/s. This is also the velocity of the tennis ball at the top of the cliff.

Now, we can plug in this value for v_i in our equation for t and solve for it. We get t = 2 seconds.

So, the initial velocity of the tennis ball must be 20m/s for it to reach the top of the cliff in 2 seconds and collide with the golf ball.

I hope this helps. Let me know if you have any further questions.

Best,