A helicopter drops a box from 120m in the air.
a. Determine the time the box is in the air.
b. determine the velocity the box would have right before it hits the ground
c. Before the helicopter had a horizontal velocity of 55/s. Determine the distance the box will travel in the x-axis.
d. solve for the Resultant velocity that the box would impact the ground with.
I know it's a long question, but I'm really lost! Thank you! :)
No problem! I'll break down each part of the question and explain how to find the answers.
a. To determine the time the box is in the air, we can use the equation of motion for vertical motion:
h = (1/2) * g * t^2
Where:
- h is the initial height (120m)
- g is the acceleration due to gravity (9.8 m/s^2)
- t is the time the box is in the air (what we want to find)
Rearranging the equation to solve for t, we have:
t = sqrt(2h/g)
Plugging in the given values, we get:
t = sqrt(2*120/9.8) ≈ 5.02 seconds
Therefore, the box is in the air for approximately 5.02 seconds.
b. To determine the velocity the box would have right before it hits the ground, we can use the equation of motion for vertical motion:
v = g * t
Where:
- v is the velocity (what we want to find)
- g is the acceleration due to gravity (9.8 m/s^2)
- t is the time the box is in the air (5.02 seconds, as we found in part a)
Plugging in the values, we have:
v = 9.8 * 5.02 ≈ 49.2 m/s
Therefore, the box would have a velocity of approximately 49.2 m/s right before it hits the ground.
c. Before we can determine the distance the box will travel in the x-axis, we need to consider the horizontal motion. Since the horizontal velocity of the helicopter is given, we can use the formula:
d = v * t
Where:
- d is the distance (what we want to find)
- v is the horizontal velocity of the helicopter (55 m/s)
- t is the time the box is in the air (5.02 seconds, as we found in part a)
Plugging in the values, we have:
d = 55 * 5.02 ≈ 276.1 meters
Therefore, the box will travel approximately 276.1 meters in the x-axis.
d. To solve for the resultant velocity that the box would impact the ground with, we can use the Pythagorean theorem to find the magnitude of the resultant velocity:
V = √(Vx^2 + Vy^2)
Where:
- V is the resultant velocity (what we want to find)
- Vx is the horizontal velocity of the box (55 m/s, same as the helicopter's velocity)
- Vy is the vertical velocity of the box (we can calculate it using the equation Vy = g * t)
Plugging in the values, we have:
Vy = 9.8 * 5.02 ≈ 49.2 m/s
V = √(55^2 + 49.2^2) ≈ 73.8 m/s
Therefore, the box would impact the ground with a resultant velocity of approximately 73.8 m/s.
I hope this explanation helps! Let me know if you have any further questions.