Question

Jan and Len throw identical rocks off a tall building at the same time. The groundnear the building is flat. Jan throws her rock straight downward. Len throws his rockdownward and outward such that the angle between the initial velocity of the rock andthe horizon is 30◦. Len throws the rock with a speed twice that of Jan’s rock. If airresistance is negligible, which rock hits the ground first?

Answer 1

Answer:

Both the rocks land together.

Explanation:

Given:

initial speed of Jan, $u_j=v$

initial speed of Len, $u_l=2u_j=2v$

direction of velocity by Jan with respect to vertical down direction, $\theta_l=0^{\circ}$

direction of velocity by Len with respect to vertical down direction, $\theta_l=(90-30)^{\circ}=60^{\circ}$

Now velocity of the rock by Len in the vertically downward direction:

$u_l_x=u_l.\cos\theta$

$u_{lx}=2v\cos60$

$u_l_x=v$

Form the equation of motion:

$h=ut+\frac{1}{2} gt^2$

where:

$h=$ height covered by the object

$u=$ initial velocity of the object

$g=$ acceleration due to gravity

$t=$ time taken by the object to fall the height

Since the velocity of both the rocks is same in the vertical direction are thrown form the same height therefore both of the rocks will land together.