A ball is projected upward at time t = 0.0 s, from a point on a roof 10 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is Consider all quantities as positive in the upward direction. At time the velocity of the ball is closest to:
Select one:
a. +12 m/s
b. -175 m/s
c. -12 m/s
d. +175 m/s
12
To find the velocity of the ball at a certain time, we can use the equations of motion.
Since the ball is projected upward, we can assume that the acceleration due to gravity is acting in the downward direction, which is -9.8 m/s^2.
The initial velocity of the ball is the velocity at t = 0 s. Since the ball is projected upward, the initial velocity will be positive.
To find the time at which the velocity of the ball is closest to a certain value (in this case, we want to find the time when the velocity is closest to a certain sign), we can use the equation:
v = u + at
where:
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
In this case, since the final velocity is the value we want to determine and the initial velocity and acceleration are known, we need to rearrange the equation and solve for t:
t = (v - u) / a
Now let's consider each option and calculate the time for each one.
a. +12 m/s
t = (12 - initial velocity) / -9.8
b. -175 m/s
t = (-175 - initial velocity) / -9.8
c. -12 m/s
t = (-12 - initial velocity) / -9.8
d. +175 m/s
t = (175 - initial velocity) / -9.8
By substituting the known initial velocity into each equation, we can find the corresponding time for each option. The option with the smallest positive time value will be the closest to the desired sign for the velocity.