Question

A student aims a cork gun at a small dot on the wall. The wall is 10m from the students, and 8m above the level of the gun. The gun can launch corks with a speed of 12m/s. How high must the gun be aimed to hit the spot?

Answer 1

Answer:
`\theta =57.99\approx 58 ^(\circ)`

Step-by-step explanation:

Given

wall is 10 m from student

8 m high

Therefore student should launch at an angle \theta such that its maximum height is 8 m and its range is 20 m

For maximum height(h)
`=(u^2sin^2\theta )/(2g)`

Range (R)
`=(u^2sin2\theta )/(g)`

`8=(12^2sin^2\theta )/(2g)-----1`

`20=(12^2sin2\theta )/(g)----2`

divide 1 & 2

`(20)/(8)=(2sin2\theta )/(sin^2\theta )`

`(5)/(2)=(2* 2* sin\theat \cdot cos\theta )/(sin^2\theta )`

`tan\theta =(8)/(5)`

`\theta =57.99\approx 58 ^(\circ)`