Time of Flight Calculator - Projectile Motion

The following simple and easy steps are helpful to calculate the projectile time of flight. Follow these rules and guidelines to obtain an accurate answer.

• Find the details like initial height, velocity, and angle of the launch of a projectile from the question.
• Find the sin of the angle of launch value.
• If the initial height is zero, then
• Multiply the double velocity by the sin of angle of launch value.
• Divide the product by acceleration due to gravity to obtain the time of flight in the air.
• When the initial height is above zero, then multiply velocity and value from step 2.
• Square the value from the above step, add the product of 2 times acceleration due to gravity and height
• Apply square root to the above step value and add it to the product from step 6
• Divide the result by g to get the time of flight projectile motion.

If an object is thrown nearer to the earth surface, then the object would move toward's the earth's surface along a curved path with constant acceleration. That curved path is called a projectile and the motion is projectile motion. The time for which the object is in the air is called the time of flight.

When the object is launch from the ground (initial height h = 0)

Time of flight t = 2 * V_o * sin(╬▒)/g

When the object is launch from some height (initila height > 0)

Time of flight t = [V_o * sin(α) + √((V_o * sin(α))² + 2 * g * h)]/g

Where

V_o is the initial velocity

╬▒ is the angle of launch

h is the initial height

t is the time of flight.

Example

Question: A body is rojected with a velocity of 15 m/s at 60┬░ to the horzontal plane and from a height of 5 m. Find the time of flight of the projectile?

Solution:

Given that

Initial velocity V_o = 15 m/s

Angle of launch ╬▒ = 60┬░

Initial height h = 5 m

Acceleration due to gravity g = 9.8

sin(60┬░) = 0.866

Time of flight formula is t = [V_o * sin(α) + √((V_o * sin(α))² + 2 * g * h)]/g

Substitute the values in the formula

t = [15 * sin(60°) + √((15 * sin(60°))² + 2 * 9.8 * 5)]/9.8

= [15 * 0.866 + √((15 * 0.866)² + 98)]/9.8

= [12.99 + √((12.99)² + 98)]/9.8

= [12.99 + √(168.74 + 98)]/9.8

= [12.99 + √266.74]/9.8

= [12.99 + 16.33]/9.8

= 29.32/9.8

= 2.99

There, the time of flight of projectile is 2.99 seconds.

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1. What is meant by the time of flight of a projectile?

The time of flight of a projectile motion is the amount of time from the particle is projected into the air to the time it reaches the earth surface. It always depends on the velocity and angle of projection.

2. How to calculate the projectile flight time?

When the projectile is thrown from the ground, then multiply the double of initial velocity with the sin of angle of projection and divided it by acceleration due to gravity.

If the projectile is thrown from a height, then use t = [V_o * sin(α) + √((V_o * sin(α))² + 2 * g * h)]/g formula to obtain the flight time of the projectile.

3. What are the time of flight equations?

We have exactly two equations for getting the flight time of a projectile motion. They are

If the projectile is launched from zero.

Time of flight t = 2 * V_o * sin(╬▒)/g

If the projectile is launched from a height

Time of flight t = [V_o * sin(α) + √((V_o * sin(α))² + 2 * g * h)]/g

4. What factors sffect the projectile motion flight time?

The factors that sffect the time of flight are the angle of projection of the object, initial velocity of the projectile, and height of the object from the ground during the projection.

5. A body is projected with an initial velocity of 16 m/s at 35┬░ to the horizontal plane. Find the time of flight of the projectile.

Given that,

Initial velocity V_o = 16 m/s

Angle ╬▒= 35┬░

Time of flight is t = 2 * 16 * sin(35┬░)/9.8

t = 32 * 0.573/9.8 = 18.336/9.8

So, the time of flight is 1.87 seconds.