Question

A clown standing on a 23.5 m high platform tosses a ball vertically upward into the air at a speed of 6.50 m/s. The ball leaves his hand 3.40 m above the platform. (a) How high from the floor will it go? (b) Suppose the clown fails to catch the ball, with what velocity will it hit the floor?


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Answer 1

it always helps to draw it out first.use kinematics for this problem as well. we know the starting point, it's initial velocity, and since this isn't an alien clown we know it's on earth so we know acceleration. But for this problem there's two parts, i labeled them as part A and part B. part A is when the ball is going from the hand to the apex of it's trajectory and part B will be from it's apex to it's final resting point on the ground. so for part A we just need to list what we know. leaving t value(he hand it has an initial velocity of 6.5 m/s. we know a is going to be 9.8 m/s^2. and also since the measurement will be focused on the final y being at the apex we know that the final velocity will be 0. we also know the initial y value (y because it's movie in a vertical trajectory) and we just need to find it's final y value. now we have almost everything except time. so which of these can we find the final y position without the time variable?\[\Delta y=v_0t+\frac{1}{2}at^2\]\[v^2=v_0^2+2a\Delta y\]\[v=v_0+at\]\[\Delta y=\frac{v_0+v}{2}t\]also remember that\[\Delta y=y-y_0\]and keep in mind that all the vertical distances for part A can be ignored (except for h, that's what were looking for) based on where you choose to put your point of reference. if you start from the ground that's a lot of unnecessary numbers to keep around but if you place the point of reference when the ball leaves the ground our initial y value will become zero. so solve for your final y value which is also h. that will be the height the ball rises to after it leaves from the clown's hand but the question is asking for the ball's placement above the platform so it would be h+3.4