An object is released from an airplane which is driving at an angle of 30 degrees Celsius from the horizontal with a speed of 50m/s. If the plane is at a height of 4000m from the ground when the object is released, find;
(A). The velocity of the object when it hits the ground.
(B). The time taken for the object to hit the ground.
To solve this problem, we can break down the initial velocity of the object into horizontal and vertical components.
Let's first find the horizontal component of the velocity:
Horizontal component of velocity = initial velocity * cos(angle)
Horizontal component of velocity = 50 m/s * cos(30°)
Horizontal component of velocity = 50 m/s * √3/2
Horizontal component of velocity = 25√3 m/s
Now let's find the vertical component of the velocity:
Vertical component of velocity = initial velocity * sin(angle)
Vertical component of velocity = 50 m/s * sin(30°)
Vertical component of velocity = 50 m/s * 1/2
Vertical component of velocity = 25 m/s
Since the object is released from the airplane, its initial vertical velocity is 25 m/s downwards (negative direction).
The acceleration due to gravity is -9.8 m/s², directed downwards.
(A) The velocity of the object when it hits the ground will have the same horizontal component as its initial velocity and a different vertical component due to the effect of gravity. The horizontal component will remain unchanged at 25√3 m/s. The vertical component will be affected by gravity as follows:
Final vertical velocity = initial vertical velocity + (acceleration due to gravity * time)
0 m/s = -25 m/s + (-9.8 m/s² * time)
Solving for the time:
25 m/s = 9.8 m/s² * time
time = 25 m/s / 9.8 m/s²
time ≈ 2.55 seconds
Therefore, the time taken for the object to hit the ground is approximately 2.55 seconds.
(B) To find the velocity of the object when it hits the ground, we can use the time calculated in part (A) and the horizontal component of velocity:
Velocity = horizontal component of velocity
Velocity = 25√3 m/s
Therefore, the velocity of the object when it hits the ground is exactly 25√3 m/s.