An aeroplane is flying horizontally at a height of 980m with a velocity 100m/s drops a food packet .a person on the ground who is initially 414m ahead of the point of projection with what velocity should he move so that he catches the food packet ?

Question

Answer

20.27m/s

Answer

Introduction:
In this problem, an airplane is flying horizontally at a height of 980m with a velocity of 100m/s. The airplane drops a food packet, and a person on the ground, who is initially 414m ahead of the point of projection, wants to catch the food packet. We need to determine the velocity with which the person should move in order to catch the food packet.

Given:
- Height of the airplane (h) = 980m
- Velocity of the airplane (v) = 100m/s
- Initial distance of the person ahead of the point of projection (d) = 414m

Approach:
To calculate the velocity with which the person should move, we will first find the time taken by the food packet to reach the ground. Then we will calculate the horizontal distance traveled by the food packet during that time. Finally, we will determine the velocity of the person required to cover that horizontal distance in the same time.

Calculations:

Step 1: Find the time taken by the food packet to reach the ground.
- The vertical motion of the food packet can be calculated using the equation: h = (1/2)gt^2, where g is the acceleration due to gravity (9.8m/s^2).
- Substituting the given values: 980 = (1/2)(9.8)t^2
- Solving for t, we get t = √(2h/g) = √(2*980/9.8) = 20s

Step 2: Calculate the horizontal distance traveled by the food packet.
- The horizontal distance traveled by the food packet can be calculated using the equation: d = vt, where v is the horizontal velocity of the airplane.
- Substituting the given values: d = 100 * 20 = 2000m

Step 3: Determine the velocity of the person required to cover the horizontal distance in the same time.
- The velocity of the person can be calculated using the equation: v = d/t, where d is the horizontal distance traveled by the food packet and t is the time taken.
- Substituting the calculated values: v = 2000/20 = 100m/s

Conclusion:
The person on the ground should move with a velocity of 100m/s in order to catch the food packet dropped from the airplane.

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