Question

During a snowball fight , your opponent distracts you by throwing a snowball at you in a high arc. she thriws snowballs with a speed of 24.5 m/s and the first is thrown at 70.0 degrees. As you are watching the first snowball, she throws a second at a lower angle. If both snowballs cover the same horizontal distance, at what angle should the second be thrown?

Answer 1

Step-by-step explanation:

Given

launch velocity
`u=24.5\ m/s`

first ball launch angle
`\theta _1=70^(\circ)`

Suppose another ball is thrown at an angle of
`\theta _2`

Both ball have same range

Range of Projectile
`R=(u^2\sin 2\theta )/(g)`

`R_1=(u^2\sin 2\theta _1)/(g)`

For second ball

`R_2=(u^2\sin 2\theta _2)/(g)`

`R_1=R_2`

`(u^2\sin 2\theta _1)/(g)=(u^2\sin 2\theta _2)/(g)`

`\sin 2\theta _1=\sin 2theta _2`

Either
`\theta _1=\theta _2` or

`2\theta _1=180-2\theta _2`

I.e.
`\theta _2=90-\theta _1`

`\theta _2=90-70=20^(\circ)`

so another ball must be thrown at
`20^(\circ)`