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

Step-by-step explanation:

Maximum height of a projectile

`H_(max)=(u^2\sin ^2\theta )/(2g)`

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

`\theta =35.7^(\circ)`

`H_1=(30.7^2* \sin ^2(35.7))/(2* 9.8)`

`H_1=16.37\ m`

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

`\theta =33.2^(\circ)`

`H_2=(47.9^2* \sin ^2(33.2))/(2* 9.8)`

`H_2=35.09\ m`

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

`\theta =67.7^(\circ)`

`H_3=(21.8^2* \sin ^2(67.7))/(2* 9.8)`

`H_3=20.75\ m`

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

`\theta =62.1^(\circ)`

`H_4=(7.7^2* \sin ^2(62.1))/(2* 9.8)`

`H_4=2.36\ m`

Therefore height reached by pumpkin can be arranged as

`H_4<H_1<H_3<H_2`