# A ball is thrown upwards

• November 10th 2008, 10:10 AM
andythefox
A ball is thrown upwards
Hey I am doing some exam questions from a mechanics textbook and I am really confused I was just wondering if anyone could help me out The question is:

A ball is thrown upwards at 7ms from a point A which is 8m vertically above horizontal ground. Given that the ball moves freely under gravity find:

the greatest height above the ground attained by the ball

the speed of the ball the instant it when it strikes the ground

Thanks alot :)

A ball is thrown vertically upwards and takes 3 seconds to reach its highest point. Find the times at which the ball is 39.2m above its point of projection.
• November 10th 2008, 11:23 PM
Kiwi_Dave
Define the origin to be at ground level and up to be the positive direction. Let the position be called s, velocity v and acceleration a.

We have a = -9.81 m/s/s due to gravity.
$s_0=8, v_0=7$
equation 1. $s=s_0+v_0t+0.5at^2$
equation 2. $v=v_0+at$

Now when the ball is at its highest it is neither going up nor down, that is v=0. So set equation 2 equal to zero and solve it for t, the time at which the height is maximum. Substitute this value of t into equation 1 to find the maximum height.

For the second part set equation 1 equal to zero and solve for t, the time at which the ball hits the ground. Substitute this into equation 2 to find the velocity when the ball hits the ground. Since we defined the positive direction to be up, the answer will be negative.

For your second question $s_0=0$, v_0 is not known. Use equation 2 with t=3 to find v_0, then you can find the required answer using equation 1 by solving for the only unknown (t).
• November 11th 2008, 11:41 PM
andythefox
thanks alot (Rofl)