A parachutist with a camera, both descending at a speed of 9.2 m/s, releases the camera
at an altitude of 32.3 m.
What is the magitude of the velocity of the
camera just before it hits the ground? The
acceleration of gravity is 9.8 m/s
2
and air
friction is negligible.
Answer in units of m/s
How long does it take the camera to reach the
ground?
Answer in units of s
V^2=u^2+2as. v= the final velocity; u=the initial velocity (9.2 m/s; a is accel and s is distance (more accutately, displacement). Solve for v.
To find the magnitude of the velocity of the camera just before it hits the ground, we can use the equation:
v² = u² + 2as
Where:
- v is the final velocity of the camera
- u is the initial velocity of the camera (which is 9.2 m/s, same as the parachutist)
- a is the acceleration due to gravity (9.8 m/s^2)
- s is the displacement of the camera (which is the altitude of 32.3 m, as it is released at that height)
Plugging in the values, we have:
v² = (9.2 m/s)² + 2(-9.8 m/s²)(32.3 m)
v² = 84.64 m²/s² - 638.64 m²/s²
v² = -554 m²/s²
Since the magnitude of velocity cannot be negative, we take the square root of the positive value:
v = √(554 m²/s²) = 23.54 m/s
Therefore, the magnitude of the velocity of the camera just before it hits the ground is 23.54 m/s.
To find the time it takes for the camera to reach the ground, we can use the equation:
s = ut + (1/2)at²
Where:
- s is the displacement (which is the height of 32.3 m)
- u is the initial velocity of the camera (9.2 m/s)
- a is the acceleration due to gravity (-9.8 m/s², negative because it acts in the opposite direction of the motion)
- t is the time
Plugging in the values, we have:
32.3 m = (9.2 m/s)t + (1/2)(-9.8 m/s²)(t²)
32.3 m = 9.2 m/s)t - 4.9 m/s²(t²)
Rearranging the equation, we have:
4.9t² - 9.2t + 32.3 = 0
Solving this quadratic equation using the quadratic formula or factoring, we find:
t ≈ 2.03 s or t ≈ 3.35 s
Since time cannot be negative, the camera takes approximately 2.03 seconds to reach the ground.
Therefore, the magnitude of the velocity of the camera just before it hits the ground is 23.54 m/s, and it takes approximately 2.03 seconds to reach the ground.