Projectile Motion -- mountain jumper

In summary, the problem presents a jumper who runs horizontally off a 910 meter mountain with a speed of 4.0 m/s and experiences a free fall until reaching a height of 150 meters above the valley floor, at which point she opens her parachute. The task is to determine the duration of her free fall and her distance from the cliff when she opens her parachute. Using kinematic equations, the vertical component Y at the end of free fall is 150 meters, with a starting height of 910 meters and an initial vertical velocity of 0 m/s. The acceleration due to gravity is -9.8 m/s^2.
  • #1
Scorry
17
1
1. Homework Statement
A jumper runs horizontally off a 910 meter mountain with speed 4.0 m/s and enjoys a free fall until she is 150 meters above the valley floor, at which time she opens her parachute. Ignore air resistance

Homework Equations


A) how long is the jumper in free fall.

B) how far from the cliff is the jumper when she opens her parachute?

The Attempt at a Solution


My attempt is attached with kinematic equations. I want to use Y to find time.

I'm confused on Y. Is it the height 910 meters or 910 meters - 150 meters = 760 meters. Can you explain the vertical component to me?
 

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  • #2
In the case of Y = y_0 + v_0t + 1/2*at^2, your Y at the time you are interested in should be Y at the end of the free fall, or 150m.
y_0 is the starting height, v_0 is the vertical component of initial velocity (zero) and a should be -9.8m/s^2.
 
  • #3
Thank you RUber. I am about to rework it.
 

FAQ: Projectile Motion -- mountain jumper

1. What is projectile motion and how does it apply to mountain jumping?

Projectile motion is the motion of an object through the air under the influence of gravity. In mountain jumping, it applies to the movement of the jumper as they travel through the air after leaving the mountain.

2. How does the angle of launch affect the distance and height of the jump?

The angle of launch, also known as the angle of trajectory, determines the distance and height of the jump. A steeper angle will result in a shorter but higher jump, while a shallower angle will result in a longer but lower jump.

3. What factors affect the trajectory of a mountain jumper?

The trajectory of a mountain jumper is affected by the angle of launch, initial velocity, air resistance, and the force of gravity. Other factors such as wind and the shape of the mountain can also play a role.

4. How does air resistance affect the motion of a mountain jumper?

Air resistance, also known as drag, slows down the motion of a mountain jumper as they travel through the air. It is affected by the shape and size of the jumper, as well as the density of the air and the speed at which they are moving.

5. How is the distance and time of flight calculated for a mountain jumper?

The distance and time of flight for a mountain jumper can be calculated using the equations of projectile motion, which take into account the initial velocity, angle of launch, and force of gravity. These calculations can also be affected by factors such as air resistance and the shape of the mountain.

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