Question

Relative to the ground, a car has a velocity of 15.3 m/s, directed due north. Relative to this car, a truck has a velocity of 22.5 m/s, directed 52.0° north of east. What is the magnitude of the truck's velocity relative to the ground

Answer 1

Answer:

The magnitude of the truck's velocity relative to the ground is 35.82 m/s.

Explanation:

Given that,

Velocity of car relative to ground = 15.3 m/s

Velocity of truck relative to car = 22.5 m/s

We need to calculate the magnitude of the truck's velocity relative to the ground

We need to calculate the x component of the velocity

$v_{x}=22.5\cos\theta$

$v_{x}=22.5\cos52^{\circ}$

$v_{x}=13.852\ m/s$

We need to calculate the y component of the velocity

$v_{y}=15.3+22.5\sin\theta$

$v_{y}=15.3+22.5\sin52^{\circ}$

$v_{y}=33.030\ m/s$

Using Pythagorean theorem

$|v|=\sqrt{v_{x}^2+v_{y}^2}$

$|v|=\sqrt{(13.852)^2+(33.030)^2}$

$|v|=35.82\ m/s$

Hence, The magnitude of the truck's velocity relative to the ground is 35.82 m/s.