Question

"What is its time interval between the release of the ball and the time it reaches its maximum height? Its initial vertical speed is 11.7 m/s and the acceleration of gravity is 9.8 m/s^2. Neglect air resistance. Answer in units of s.

A) 1.2 s
B) 1.3 s
C) 1.4 s
D) 1.5 s"

Answer 1

To find the time interval for the ball to reach its maximum height with an initial speed of 11.7 m/s and gravity at 9.8 m/s^2, use the kinematic equation v = u + at. The final velocity (v) at maximum height is 0 m/s, and by rearranging the equation, the time (t) is found to be 1.2 seconds.

Step-by-step explanation:

The question relates to the concept of a ball thrown vertically upwards and the time interval it takes to reach the maximum height. We're given the initial vertical speed of the ball as 11.7 m/s and the acceleration due to gravity as 9.8 m/s2, which is a constant downward acceleration.

To find the time taken to reach maximum height, we use the kinematic equation for vertical motion without air resistance:

• v = u + at

Where:

• v is the final velocity (0 m/s at the maximum height),
• u is the initial velocity (11.7 m/s),
• a is the acceleration due to gravity (-9.8 m/s2 as it acts downwards)
• t is the time interval we are trying to find.

Setting v = 0 (since the ball stops rising at maximum height) and rearranging for t:

0 = 11.7 m/s + (-9.8 m/s2)*t

t = 11.7 m/s / 9.8 m/s2

t = 1.2 s

So, the correct answer is (A) 1.2 s.