A ball, initially at y = 0, is thrown straight down and takes 1.50 s to move 15.5 m in the - y direction. Calculate the initial velocity of the ball.
Calculate the velocity of the ball at t = 0.900s.
To calculate the initial velocity of the ball, we can use the formula for constant acceleration motion:
y = y0 + v0*t + (1/2)*a*t^2
where:
- y is the final position of the ball (15.5 m),
- y0 is the initial position of the ball (0 m),
- v0 is the initial velocity of the ball (which we want to find),
- t is the time taken for the ball to move (1.50 s),
- and a is the acceleration of the ball (which we'll assume is due to gravity, -9.8 m/s^2 in the downward direction).
We can rearrange the formula and solve for v0:
v0 = (y - y0 - (1/2)*a*t^2) / t
Plugging in the given values:
v0 = (15.5 m - 0 m - (1/2)*(9.8 m/s^2)*(1.50 s)^2) / 1.50 s
v0 = (15.5 m - 11.025 m) / 1.50 s
v0 = 4.475 m / 1.50 s
v0 = 2.9833 m/s
Therefore, the initial velocity of the ball is approximately 2.9833 m/s.
To calculate the velocity of the ball at t = 0.900 s, we can use the formula for velocity in constant acceleration motion:
v = v0 + a*t
where:
- v is the velocity of the ball at time t (which we want to find),
- v0 is the initial velocity of the ball (2.9833 m/s),
- a is the acceleration of the ball (-9.8 m/s^2),
- and t is the time at which we want to calculate the velocity (0.900 s).
Plugging in the given values:
v = 2.9833 m/s + (-9.8 m/s^2) * 0.900 s
v = 2.9833 m/s - 8.82 m/s
v = -5.8367 m/s
Therefore, the velocity of the ball at t = 0.900 s is approximately -5.8367 m/s.