Question

1.) A ski jump is angled at 40° and the skier is launched at 25 m/s. A.) What was her highest

Answer 1

A) 13.2 m

The motion of the skier is a projectile motion, which consists of two independent motions:

- a horizontal motion with constant speed

- a vertical motion with constant acceleration $g=-9.8 m/s^2$ (acceleration of gravity) downward

To find the maximum height of her trajectory, we are only concerned with her vertical motion.

The initial vertical velocity upward is

$u_y = u_0 sin \theta = (25) sin 40^{\circ} =16.1 m/s$

then we can use the following SUVAT equation:

$v_y^2 - u_y^2 = 2ah$

where

$v_y=0$ is the final vertical velocity, which is zero at the maximum height

$u_y = 16.1 m/s$ is the initial vertical velocity

$a=g=-9.8 m/s^2$

h is the maximum height

Solving for h,

$h=\frac{v_y^2-u_y^2}{2g}=\frac{-(16.1)^2}{2(-9.8)}=13.2 m$

B) 1.64 s

The time needed to reach the highest point can be found by analyzing again the vertical motion only. In fact, we can use the  following SUVAT equation:

$v_y = u_y +at$

where

$u_y = 16.1 m/s$

$a=g=-9.8 m/s^2$

At the maximum height, the vertical velocity is zero:

$v_y=0$

So we can solve the equation to find the corresponding time:

$t=\frac{v_y-u_y}{a}=\frac{0-16.1}{-9.8}=1.64 s$