Aslingshot can project a pebble at a speed as high as 38.0 m/s. (a) if air resistance can be ignored, how high (in m) would a pebble launched at this speed rise if projected straight up?

73.67 m

Explanation:

If projected straight up, we can work in 1 dimension, and we can use the following kinematic equations:

,

Where its our initial height,  our initial speed, a the acceleration and t the time that has passed.

For our problem, the initial height its 0 meters, our initial speed its 38.0 m/s, the acceleration its the gravitational one ( g = 9.8 m/s^2), and the time its uknown.

We can plug this values in our equations, to obtain:

note that the acceleration point downwards, hence the minus sign.

Now, in the highest point, velocity must be zero, so, we can grab our second equation, and write:

and obtain:

Plugin this time on our first equation we find: