A stone is dropped from a balloon going up with a uniform velocity of 5 M per second. If the balloon was 50 M high when the stone was dropped, find it height stone hits the ground
find the time for the stone to reach the ground ... 0 = -4.9 t^2 + 5 t + 50
multiply the time by the balloon's velocity , and add 50 m
68
To find the height at which the stone hits the ground, we need to calculate the time it takes for the stone to fall and then plug that value into the equation for calculating distance.
Step 1: Calculate the time it takes for the stone to fall.
When the stone is dropped, it will accelerate due to gravity. The initial velocity is 5 m/s, but since it's going up, we consider it negative (-5 m/s). The acceleration due to gravity is approximately 9.8 m/s^2 and is assumed to be negative as well (since it acts downward).
We can use the following formula to calculate the time it takes for an object to fall:
time = 2 * (final height / acceleration due to gravity)^0.5
In this case, the final height is 50 m and the acceleration due to gravity is -9.8 m/s^2.
time = 2 * (50 / 9.8)^0.5
= 2 * (5.102)^0.5
≈ 2 * 2.26
≈ 4.52 s
Step 2: Calculate the height at which the stone hits the ground.
To calculate the height, we can use the following formula:
height = initial velocity * time + 0.5 * acceleration * time^2
In this case, the initial velocity is -5 m/s, the acceleration is -9.8 m/s^2, and the time is 4.52 s.
height = -5 * 4.52 + 0.5 * -9.8 * 4.52^2
≈ -22.6 + 0.5 * -9.8 * 20.4304
≈ -22.6 + 0.5 * -9.8 * 418.090496
≈ -22.6 + 2070.643712
≈ 2048.043712
Therefore, the height at which the stone hits the ground is approximately 2048.04 m.