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

Answer:

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

Explanation:

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

$R=\frac{u^2.sin\ \2\theta}{g}$

where:

u = initial velocity of the projectile

$\theta =$ angle of projection of projectile

Now, range for ball 1 :

$d_1=\frac{u^2.sin\ \2\theta}{g}$

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

$d_2=\frac{(2u)^2.sin\ \2\theta}{g}$

$d_2=4\times \frac{u^2.sin\ \2\theta}{g}$

$d_2=4\times d_1$