Question

A train is travelling east along a straight run of track at 54.0 km/hr. Inside, two siblings 1.90 m apart are playing catch directly across the aisle. The kid wearing a Catherine Wheel T-shirt throws the ball horizontally north. The ball crosses the train and is caught 1.05 s later by her little brother. (Ignore any effects of gravity or friction.)

a) Find the magnitude of the ball's velocity from the little brother's point of view.
b) What is the magnitude of the velocity of the ball as seen by someone standing still outside the train?
c) What is the angle between the direction of the ball and the direction of the train as measured by someone standing still outside the train?

Answer 1

A.) 1.81 m/s

B.) 16.07 m/s

C.) 6.88 degree.

Step-by-step explanation:

Given that Inside, two siblings 1.90 m apart are playing catch directly across the aisle. The kid wearing a Catherine Wheel T-shirt throws the ball horizontally north. The ball crosses the train and is caught 1.05 s later by her little brother.

The velocity of the ball will be

Velocity = displacement/ time

Where displacement = 1.90 m

Time = 1.05 s

Velocity = 1.9 / 1.05

Velocity = 1.8095

Velocity = 1.81 m/s

A.) From the little brother point of view, the magnitude of ball's velocity will be 1.81 m/s

B.) The magnitude of the velocity of the ball as seen by someone standing still outside the train will be achieved by first converting km/h to m/s

(54 × 1000) / 3600 = 15 m/s

Then, use pythagorean theorem to find the velocity

V = sqrt ( 15^2 + 1.81^2)

V = sqrt ( 225 + 3.2761)

V = sqrt ( 258.2761)

V = 16.07 m/s

C.) The angle will be

Tan Ø = 1.81 / 15

Tan Ø = 0.1206666

Ø = tan^-1(0. 1206666)

Ø = 6.88 degree.