An object thrown vertically up from the ground passes the height 5 metre twice in an interval of 10 seconds. What is the time of flight?

Question

An object thrown vertically up from the ground passes the height 5 metre twice in an interval of 10 seconds. What is the time of  flight?

Answer

Problem

Solution

Understanding the Problem

Before solving the problem, let's first understand the meaning of the terms used in the problem statement:

Vertical motion: Motion of an object in the vertical direction (upward or downward) is called vertical motion.

Height: The distance of the object from the ground is called height.

Interval: The time difference between two events is called interval.

Time of flight: The total time taken by an object to reach its maximum height and then return to the ground is called the time of flight.

Approach to Solve

The approach to solving this problem involves the following steps:

Determine the time taken by the object to reach the maximum height for the first time.

Calculate the total time of flight by multiplying the time taken to reach the maximum height by 2.

Calculating the Time Taken to Reach the Maximum Height

Let's assume that the object is thrown vertically upward with an initial velocity u. When the object reaches its maximum height, its final velocity becomes zero. We can use the following equation of motion to calculate the time taken to reach the maximum height:

Final velocity (v) = Initial velocity (u) + Acceleration (a) x Time (t)

At maximum height, the final velocity (v) is zero. The acceleration (a) is the acceleration due to gravity, which is -9.8 m/s2 (negative because it acts in the opposite direction to the motion). The initial velocity (u) is the velocity at which the object is thrown upward. Therefore, the equation becomes:

0 = u - 9.8 x t₁

Solving for t₁, we get:

t₁ = u/9.8

Calculating the Time of Flight

The time of flight is the time taken by the object to reach its maximum height and then return to the ground. Since the object passes the height of 5 metre twice in an interval of 10 seconds, we can say that it takes 5 seconds to reach the maximum height and another 5 seconds to return to the ground. Therefore, the total time of flight is:

Time of flight = t₁ x 2 + 5

Final Answer

Substituting the value of t₁ in the above equation, we get:

Time of flight = 2u/9.8 + 5

Therefore, the time of flight of the object thrown vertically up from the ground is 2

Answer

2 sec

Answer

5

Answer

10

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