Question

A small pumpkin is launched from a very versatile catapult at a variety of speeds and angles. The angles are measured relative to the horizontal. Rank each of the following trials by the maximum height reached by the pumpkin. (1=highest) Consider air resistance to be negligible.
1 2 3 4 Speed: 30.7m/s, Angle: 35.7°
1 2 3 4 Speed: 47.9m/s, Angle: 33.2°
1 2 3 4 Speed: 21.8m/s, Angle: 67.7°
1 2 3 4 Speed: 7.7m/s, Angle: 62.1°

Answer 1

Answer:

Explanation:

Maximum height of a projectile

$H_{max}=\frac{u^2\sin ^2\theta }{2g}$

(1)$u=30.7\ m/s$

$\theta =35.7^{\circ}$

$H_1=\frac{30.7^2\times \sin ^2(35.7)}{2\times 9.8}$

$H_1=16.37\ m$

(2)$u=47.9\ m/s$

$\theta =33.2^{\circ}$

$H_2=\frac{47.9^2\times \sin ^2(33.2)}{2\times 9.8}$

$H_2=35.09\ m$

(3)$u=21.8\ m/s$

$\theta =67.7^{\circ}$

$H_3=\frac{21.8^2\times \sin ^2(67.7)}{2\times 9.8}$

$H_3=20.75\ m$

(4)$u=7.7\ m/s$

$\theta =62.1^{\circ}$

$H_4=\frac{7.7^2\times \sin ^2(62.1)}{2\times 9.8}$

$H_4=2.36\ m$      

Therefore height reached by pumpkin can be arranged as

$H_4$