Question

A semi-trailer is coasting downhill along a mountain highway when its brakes fail. The driver pulls onto a runaway truck ramp that is inclined at an angle of 17.0° above the horizontal. The semi-trailer coasts to a stop after traveling 160 m along the ramp. What was the truck's initial speed?

Answer 1

Answer:

The velocity is 30.279 m/s

Explanation:

Consider the initial speed of the semi-trailer be v

Then, initial kinetic energy = $\frac{1}{2} mv^2$

According to question, the semi-trailer coast along a ramp, which is inclined at an angle of 170, and to a distance of 160m to stop

Change in vertical position =$h=160 \times \sin 17^{\circ}-0$= 46.779m

Final potential energy of semitrailer = mgh

Applying principle of conservation of energy,

$\frac{1}{2} mv^2$ = mgh

Solving for v, we get $v^2$ = 2gh = 2*9.8*46.779 = 916.8684

$v^2$ = 916.8684

v = 30.279 m/s

Therefore, the velocity is 30.279 m/s