A basketball rolls to the right with a velocity of 4 meters per second. It is pushed up and accelerated up for 2 seconds with an acceleration of 4 meters per second . Then for 1 second it is pushed and accelerated down with an acceleration of 12 meters per second . What is its final velocity and in exactly what direction
NOTE - acceleration is in m/s^2 NOT m/s
Its horizontal velocity component does not change since there is no horizontal force
u = 4 m/s
Vertical
Vi = 0
v = Vi + a t
v = 0 + 4 * 2 = 8 m/s
v = 8 - 12 (1) = -4 m/s
so in the end
u = 4 and v = -4
speed = 4 sqrt 2
direction = 45 degrees down from horizontal
To find the final velocity and direction of the basketball, we need to break down the problem into three parts: the initial velocity, the acceleration, and the time duration.
1. Initial velocity: The basketball rolls to the right with a velocity of 4 meters per second. This means the initial velocity is +4 m/s (positive because it's to the right).
2. Acceleration and duration:
a) During the first 2 seconds, the basketball is pushed and accelerated up with an acceleration of +4 meters per second. This means the acceleration is +4 m/s^2 (positive because it's in the upward direction) and the time duration is 2 seconds.
b) During the next 1 second, the basketball is pushed and accelerated down with an acceleration of -12 meters per second. This means the acceleration is -12 m/s^2 (negative because it's in the downward direction) and the time duration is 1 second.
To calculate the final velocity of the basketball, we need to use the equation:
Final velocity = Initial velocity + (Acceleration x Time)
Now, let's calculate the final velocity for each part:
1. During the first 2 seconds:
Initial velocity = +4 m/s
Acceleration = +4 m/s^2
Time = 2 s
Final velocity = 4 m/s + (4 m/s^2 x 2 s)
= 4 m/s + 8 m/s
= 12 m/s
2. During the next 1 second:
Initial velocity = 12 m/s (from the previous calculation)
Acceleration = -12 m/s^2
Time = 1 s
Final velocity = 12 m/s + (-12 m/s^2 x 1 s)
= 12 m/s - 12 m/s
= 0 m/s
Therefore, the final velocity of the basketball is 0 m/s. Since it started rolling to the right initially and then stops, the direction of the final velocity can be described as "not moving" or simply at rest.