Calculating Body Projection: Time, Height & Range

In summary, a body projected from ground level at an angle of 30 degrees with a speed of 24 m/s, neglecting air resistance and taking gravity to be 10 m/s, will reach its highest point in 1.2 seconds, reaching a height of 7.2 m. Its horizontal range will be 49.9 m.
  • #1
ProPM
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A body is projected from ground level with a speed of 24 m/s at an angle of 30 degrees above the horizontal. Neglect air resistance and take gravity to be 10 m/s. Calculate:

a) The time taken to reach its highest point
b) The greatest height reached
c) The horizontal range of the body

a) v = u + at
0 = 12 + (-10 x t)
10t = 12
t = 1.2 seconds

b) s = ut + 1/2at^2
s = (12 x 1.2) + (1/2 x -10 x 1.2^2)
s = 7.2 m

c) s = Vertical Velocity (cos 30 x 24) x t

t = 2.4

s = 49.9 m

I tried them, but I am not sure if I made any mistakes.

Can anyone help me?

Thanks!
 
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  • #2
Those answers are all correct (assuming g = -10).
 

1. How do you calculate body projection?

Body projection is calculated by using the equation d=1/2gt^2, where d is the distance projected, g is the acceleration due to gravity (9.8 m/s^2), and t is the time. This equation assumes that the body is projected from the ground with no initial velocity.

2. What factors affect the time, height, and range of body projection?

The time, height, and range of body projection are affected by the initial velocity, angle of projection, and air resistance. A greater initial velocity and a higher angle of projection will result in a longer time of flight, greater height, and greater range. Air resistance can also act as a force to slow down the body and decrease the time, height, and range of projection.

3. Can you calculate body projection on an inclined surface?

Yes, body projection on an inclined surface can be calculated by using the horizontal and vertical components of the initial velocity. The horizontal component will determine the range of projection, while the vertical component will determine the height of projection.

4. How is body projection different in different environments?

The environment can affect body projection in terms of air resistance and the acceleration due to gravity. In a vacuum, there is no air resistance, so the body will travel further and remain in the air longer. On a planet with a higher gravitational pull, the body will fall to the ground faster and have a shorter time of flight compared to a planet with a lower gravitational pull.

5. Why is calculating body projection important in sports and physics?

Calculating body projection is important in sports to determine the best angle and velocity for optimal performance. In physics, it is used to understand the motion of objects and apply principles of projectile motion to real-world scenarios. It is also a fundamental concept in the study of gravity and motion.

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