A watermelon cannon fires a watermelon vertically up into the air at a velocity of +9.5m/s, starting from an initial position of 1.2m above the ground. When the watermelon reaches the peak of its flight, what is the velocity, the acceleration, the elapsed time, and the height above the ground?
time up = t = v / g
at peak
... v = 0 ... a = g
h = [vi^2 / (2 g)] + 1.2
To find the velocity, acceleration, elapsed time, and height above the ground when the watermelon reaches the peak of its flight, we can use the equations of motion.
1. Velocity at the peak:
The velocity at the peak of the flight is equal to 0 because at the highest point, the watermelon momentarily comes to a stop before reversing its direction. Since the watermelon is moving upwards with an initial velocity of +9.5m/s, the acceleration due to gravity causes it to gradually slow down until it reaches 0 velocity.
2. Acceleration:
The acceleration due to gravity is constant and equal to -9.8 m/s² (assuming no air resistance). This negative acceleration is acting to slow down the watermelon as it moves upwards.
3. Elapsed time:
To find the elapsed time, we can use the equation:
velocity = initial velocity + (acceleration * time)
At the peak of the flight, the velocity is 0, so we have:
0 = +9.5 + (-9.8 * time)
Solving this equation, we find the value of time when the velocity is 0.
4. Height above the ground:
To determine the height above the ground at the peak of the flight, we can use the equation:
height = initial height + (initial velocity * time) + (0.5 * acceleration * time²)
At the peak of the flight, the height is unknown, the initial height is 1.2m, the initial velocity is +9.5m/s, and the time is the value we calculated in step 3.
By applying these steps, we can calculate the velocity, acceleration, elapsed time, and height above the ground when the watermelon reaches the peak of its flight.
AT the peak, its veloicty is zero, acceleration is -9.8m/s^2
vf^2=vi^2+2ad
d is the distance it traveled.
0=9.5^2-2*9.8*d
solve for d, then the height above ground is d+1.2m