Question

Three smart gates are evenly spaced on a tilted track. The separation between two adjacent gates is 30.0cm. When a racquetball rolls down the track, it passes the top gates with a speed 0.67m/s the middle gate with a speed 0.87m/s. What is its speed (in unit of m/s) when passing the bottom gate?

Two smart gates are 40.0cm apart on a tilted track. A racquetball rolls down the track, and passes the first gate with a speed 0.74m/s, the second gate 1.47m/s. What is the acceleration (in unit of m/s²) of the ball?

Answer 1

1] Use v² = u² + 2aS

here, S = 30 cm = 0.3 m, v = 0.87 m/s and u = initial velocity = 0.67 m/s

so, (0.87)² = (0.67)² + 2a(0.3)

=> a = 0.5133 m/s²

this is the acceleration of the racquetball. Its speed when passing through the lower most gate can be found using:

V² = v² + 2aS = (0.87)² + 2(0.5133)(0.3)

=> V = 1.0319 m/s

this is the speed at the bottom gate.

2]

v² = u² + 2aS

(1.47)² = (0.74)² + 2a(0.4)

=> a = 2.0166 m/s²

this is the acceleration of the ball.