You and a friend stand on a snow-covered roof. you both throw snowballs from an elevation of 15 m with the same initial speed of 13 m/s, but in different directions. you throw your snowball downward, at 40° below the horizontal; your friend throws her snowball upward, at 40° above the horizontal. what is the speed of each ball when it is 5.0 m above the ground? (neglect air resistance.)

Refer to the diagram shown below.

g = 9.8 m/s², and air resistance is ignored.

Let us consider the two trajectories.

Case A; The ball is launched 40° below the horizontal

u = (13 m/s) * cos 40° = 9.9586 m/s, the horizontal velocity

v = - (13 m/s) * sin 40° = - 8.3562 m/s

When the ball is at 5 m above ground, it would have traveled 10 m.

The vertical downward velocity is

V² = (-8.3562 m/s²) ² + 2 * (-9.8 m/s²) * (-10 m) = 265.826

V = + / - 16.304 m/s = > V = - 16.304 m/s (downward)

The horizontal velocity remains unchanged.

The speed of the ball is

√[ (-16.304) ² + 9.9586²] = 19.105 m/s

Case B: The ball is launched 40° above the horizontal.

u = 9.9586 m/s, as in case A

v = 8.3562 m/s

When the ball is 5 m above ground, the vertical velocity, V, is given by

V² = (8.3562 m/s) ² + 2 * (-9.8 m/s²) * (-10 m) = 265.826

V = + / - 16.304 m/s

The speed of the ball is

√[ (-16.304) ² + 9.9586²] = 19.105 m/s

Surprisingly, both speeds are the same.

Answer:

The speed of the ball when it is 5 m above ground is 19.1 m/s (both cases).