Question

An 800-kg car is towed up an 8º hill by a rope attached to a truck. The tension
in the rope is 2000 N, and there is no frictional resistance to the car’s motion. How much
time is needed to tow the car for 50 m starting from rest?

Answer 1

Given that,

Mass of the car = 800 kg

Tension in rope = 2000 N

Distance = 50 m

Angle = 8°

We need to calculate the acceleration

Using Newton's second law

$F = ma$

$T-mg\sin\theta=ma$

$a=\dfrac{T-mg\sin\theta}{m}$

Put the value into the formula

$a=\dfrac{2000-800\times9.8\sin8}{800}$

$a=1.14\ m/s^2$

We need to calculate the time

Using equation of motion

$s=ut+\dfrac{1}{2}at^2$

here, u = 0

$t^2=\dfrac{2s}{a}$

Put the value into the formula

$t^2=\dfrac{2\times50}{1.14}$

$t^2=87.7$

$t=\sqrt{87.7}$

$t=9.4\ sec$

Hence, The time is 9.4 sec.