There are two identical right-triangular ramps. Their vertical faces are parallel and facing each other, separated by a horizontal distance of 5 m, and their upper ends are at the same height. The inclined surface of each ramp makes an angle of 15° with the horizontal.
A small toy car approaches the first ramp along a horizontal road and moves onto the inclined surface with constant speed. What is the minimum speed with which the car should enter the ramp so that it clears the gap and lands safely on the inclined surface of the second ramp?
Neglect air resistance. Take $𝑔=10 m/s^2$.
Solution
Solution
The car leaves the first ramp with speed u at $15^\circ$.
For the minimum speed, its projectile range must be 5 m.
$R=\frac {u^2sin 2\theta}{g}$
$\therefore 5=\frac {u^2sin30}{10}$
$\Rightarrow u = 10m/s$