Question

A snowball is thrown with an initial x velocity of 7.5 m/s and an initial y velocity of 7.5 m/s . How much time is required for the snowball to reach its highest point? (Hint: The highest point of a projectile corresponds to the time when vy,f=0.)

Answer 1

Refer to the diagram shown below.

Ignore air resistance.
At maximum height, Vy = 0.
Therefore, if the time to reach maximum height is t seconds, then
0 = ( 7.5 m/s) - (9.8 m/s²)*(t s)
t = 7.5/9.8 = 0.7653 s

Note that the horizontal distance traveled is
Vx*t = (7.5 m/s)*(0.7653 s) = 5.74 m

Answer: 0.765 s

Answer 2

We are only interested in the vertical motion of the ball, in order to solve the problem.

The vertical motion of the ball is an uniformly accelerated motion, with constant acceleration
`a=g=-9.81 m/s^2` (acceleration of gravity). Therefore, the vertical velocity at time t is given by

`v_y (t) = v_(y0) +at`

where
`v_(y0)=7.5 m/s` is the initial vertical velocity of the ball.

The ball reaches its highest point when
`v_y(t)=0`: therefore, substituting this information into the equation, we can calculate the time t at which this happens:

`0=v_(y0)+at`

`t=-(v_(0y))/(a)=-(7.5 m/s)/(9.81 m/s^2)=0.765 s`