a photographer inside a helicopter which is descending vertically at 15m/s at an altitude of 55 meters accidentally dropped his camera. how long will it take the camera to reach the ground.
2.15
To find the time it takes for the camera to reach the ground, we can use the concept of free fall and the principles of motion.
When the camera is dropped, it will experience two types of motion simultaneously: the downward motion due to being dropped from the helicopter and the vertical motion of the helicopter descending.
Let's break down the problem into two parts:
1. Vertical motion of the camera due to being dropped:
When the camera is dropped, it will fall under the force of gravity, accelerating downwards at a rate of 9.8 m/s² (acceleration due to gravity). We consider the positive direction as downward, so the acceleration is negative (-9.8 m/s²).
We can use the following equation to calculate the time it takes for the camera to fall:
h = (1/2) * g * t²
Where:
h is the height (vertical distance) the camera falls (55 meters),
g is the acceleration due to gravity (-9.8 m/s²),
t is the time it takes for the camera to fall (which we need to find).
Rearranging this equation to solve for time (t):
t = sqrt((2h) / -g)
Plugging in the given values:
t = sqrt((2 * 55) / -9.8)
Simply calculating the above expression will give us the time it takes for the camera to fall when dropped.
2. Vertical motion of the camera due to the helicopter descending:
Since the helicopter is descending vertically at a constant rate of 15 m/s, the camera will also move downwards with the same velocity.
Hence, the time taken by the camera to reach the ground will be the same as the time taken by the helicopter. We can calculate this time by dividing the distance (55 meters) by the velocity:
t = h / v
Plugging in the given values:
t = 55 / 15
Simply calculating the above expression will give us the total time taken for the camera to reach the ground.
Please note that both calculations assume there is no air resistance affecting the camera's fall.
2.14
the free-fall equation is ... h = -1/2 g t^2 - 15 t + 55
... g = 9.8
solve for t ... the positive solution