Question

Two golf balls are hit from the same point on a flat field. Both are hit at an angle of 20° above the horizontal. Ball 2 has twice the initial speed of ball 1. If ball 1 lands a distance d1 from the initial point, at what distance d2 does ball 2 land from the initial point? (Neglect any effects due to air resistance.)

A) dd_{2} = 2d_{_{1}}

B) d_{2} = 0.5d_{_{1}}

C)d_{2} = 8d_{_{1}}

D) d_{2} = d_{_{1}}

E) d_{2} = 4d_{_{1}}

Answer 1

E) d_{2} = 4d_{_{1}}

Step-by-step explanation:

We know that the range of a projectile is given by:

`R=(u^2.sin\ \2\theta)/(g)`

where:

u = initial velocity of the projectile

`\theta =` angle of projection of projectile

Now, range for ball 1 :

`d_1=(u^2.sin\ \2\theta)/(g)`

Now, range for ball 2 with double velocity and all the other parameters being the same:

`d_2=((2u)^2.sin\ \2\theta)/(g)`

`d_2=4* (u^2.sin\ \2\theta)/(g)`

`d_2=4* d_1`