a fruit drops from the top of a tree 40m tall, calculate. the time taken to reach the ground. the velocity just before it hits the ground.
40 = (1/2)(9.81) t^2
t = 2.86 seconds
v = g t = 9.81 * 2.86
To calculate the time taken for the fruit to reach the ground and the velocity just before it hits, we can use basic kinematic equations. The key equation we will use is:
1. The equation for free fall is given by:
h = (1/2)gt^2
where:
h is the height of the tree (40m),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
t is the time taken to reach the ground.
To find the time taken (t), we rearrange the equation:
t = sqrt(2h / g)
Now let's calculate the time:
t = sqrt(2 * 40 / 9.8)
t = sqrt(80 / 9.8)
t ≈ sqrt(8.16)
t ≈ 2.86 seconds (rounded to two decimal places)
Therefore, it takes approximately 2.86 seconds for the fruit to reach the ground.
To calculate the velocity just before it hits the ground, we can use another kinematic equation:
2. The equation for final velocity (v) is given by:
v = gt
where:
v is the final velocity,
g is the acceleration due to gravity (approximately 9.8 m/s^2),
t is the time taken to reach the ground (2.86 seconds).
Now, let's calculate the final velocity:
v = 9.8 * 2.86
v ≈ 28 m/s (rounded to two decimal places)
Therefore, the velocity of the fruit just before it hits the ground is approximately 28 m/s.