Uniform Acceleration/Projectile Motion

In summary, a long jumper's jump of 7.5m and 0.8s in the air with a centre of gravity drop of 0.95m can be used to calculate the horizontal velocity at take-off, which is 9.38m/s. By using the equation d = v1*t + (1/2)at^2 for the vertical direction, the vertical velocity at take-off can be found to be 2.7(3) m/s, and from this, the angle at which the long jumper projects himself at take-off can be calculated.
  • #1
barnaby
17
0

Homework Statement


"A long jumper's jump measures 7.5m, and he is in the air for 0.8s. His centre of gravity falls 0.95m between his take off and landing."

a) Calculate his horizontal velocity at take-off.
b) Show that his vertical velocity is 2.7(3) m/s.
c) Hence calculate the angle at which he projects himself at take-off.

Homework Equations



[tex] v_{ave} = \Delta x / \Delta t [/tex]
[tex] v_{horiz.} = v_{result.}cos \Theta [/tex]
[tex] v_{vert.} = v_{result.}sin \Theta [/tex]

There may be some more that have to come into use, too...

The Attempt at a Solution



I calculated that his horizontal velocity at take-off is 9.38m/s, since he travels 7.5m horizontally in 0.8s.

I have spent about an hour trying to work out what to calculate, and how, in order to be able to calculate the vertical velocity at take-off.

I tried to calculate his instantaneous velocity at the point where his centre of gravity had reached its original point, but I couldn't since I don't know the angle at which he was projected...

It all goes downhill from here, really.

Any help would be greatly appreciated.

Thanks a lot.
 
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  • #2
d = v1*t + (1/2)at^2

apply this equation for the vertical direction. you have t, a and d. you can solve for v1.
 
  • #3
Oh, of course... the centre of gravity thing threw me a bit. Thanks!
 
Last edited:
  • #4
barnaby said:
Oh, of course... the centre of gravity thing threw me a bit. Thanks!

No prob. just use d = -0.95m
 

1. What is uniform acceleration?

Uniform acceleration is a type of motion where an object moves in a straight line with a constant rate of change in velocity. This means that the object's speed increases or decreases by the same amount in each unit of time.

2. What is projectile motion?

Projectile motion is a type of motion in which an object is projected into the air and moves along a curved path under the influence of gravity. This type of motion can be seen in everyday examples such as throwing a ball or shooting a basketball.

3. How is uniform acceleration related to projectile motion?

Uniform acceleration is a component of projectile motion. When an object is in projectile motion, it experiences both horizontal and vertical motion. The horizontal motion is typically uniform, while the vertical motion is influenced by gravity, resulting in a parabolic trajectory.

4. What factors affect the trajectory of a projectile?

The trajectory of a projectile is affected by several factors, including the initial velocity, angle of projection, and air resistance. These factors can change the shape and distance of the projectile's path.

5. How can we calculate the range of a projectile?

The range of a projectile can be calculated using the equation R = (V^2 * sin(2θ)) / g, where R is the range, V is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity. This equation assumes that air resistance is negligible.

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