Calculate the displacement and velocity at time of 0.5secs for a ball thrown straight up with an initial velocity of 15m/s.
v = Vi - g t
= 15 - 9.81 (.5)
= 10.1 m/s
h = Vi t - 4.9 t^2
= 15 (.5) -4.9(.25)
To calculate the displacement and velocity of a ball thrown straight up, we can use the equations of motion.
Let's start with the equation for displacement:
Displacement (d) = Initial Velocity (v₀) × Time (t) + 0.5 × Acceleration (a) × Time (t)²
For a ball thrown straight up, the initial velocity is positive (+15m/s) as it moves upward. The acceleration due to gravity is always negative (-9.8m/s²) as it opposes the motion of the ball. The time given is 0.5 seconds.
Plugging in the values:
d = (15m/s) × (0.5s) + 0.5 × (-9.8m/s²) × (0.5s)²
d = 7.5m - 1.225m
d = 6.275m (rounded to three decimal places)
Therefore, the displacement of the ball at 0.5 seconds is approximately 6.275 meters.
Now, let's calculate the velocity at 0.5 seconds.
Velocity (v) = Initial Velocity (v₀) + Acceleration (a) × Time (t)
Plugging in the values:
v = (15m/s) + (-9.8m/s²) × (0.5s)
v = 15m/s - 4.9m/s
v = 10.1m/s (rounded to one decimal place)
Therefore, the velocity of the ball at 0.5 seconds is approximately 10.1 meters per second.