Projectile Motion of a grasshopper off a cliff

In summary, the conversation is about finding the height of a vertical cliff using information from a figure of a grasshopper leaping from the edge. The initial speed of the grasshopper is found to be 1.5m/s and the equations used include h = ut + (1/2)gt2 and x = vt. The conversation also discusses separating the vertical and horizontal motion and using the ratios of initial velocities to solve the problem. Ultimately, the solution involves using the horizontal distance to find the time of flight and then using the vertical distance to find the total height of the cliff.
  • #1
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Homework Statement



A grasshopper leaps into the air from the edge of a vertical cliff, as shown in the figure below.

1012348.jpg



Homework Equations



Use information from the figure to find the height of the cliff.

The Attempt at a Solution



The first question was to find the initial speed of the grasshopper. I found this to be 1.5m/s.

I have tried using this equation to get the height of the cliff but it isn't right:

h = ut + (1/2)gt2 where u is the initial velocity. Any help is greatly appreciated.
 
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  • #2
How did you get the 1.5 m/s?
You must separate the vertical and horizontal motion - they are independent.
Make two headings "horizontal" and "vertical". Write x = vt under the horizontal heading and the accelerated motion formulas under the vertical heading. Fill in all the numbers you have. Note that while you don't know the initial Vx or Vy, you do know their ratio, so enter Vx as an unknown and then Vy as Vx times a tangent. If you have only one unknown in one of the formulas, begin with that! If not, you'll have to use 2 or 3 of them and solve as a system of equations.

Show your equations here if you would like more help!
 
  • #3
Well to get the components of the velocity it is just 1.5sin(50) and 1.5cos(50) so can I just use the y-component and plug that into the formula to find the total distance traveled in the y direction?
 
  • #4
Okay, I found the 1.5 too. Tricky calc!
I think you will have to use the horizontal distance first - it matters. Use it to find the time of flight and then use the vertical part to find the vertical distance.
 
  • #5
Okay I got the total time to be 1.0993 s. I used this :

t = 1.06 m / (1.5cos 50)

Not sure where to go to from here...
 
  • #6
Bah, I got it. Just use that time, then the y-component and use the equation:

x = x0 + V0xt + 1/2axt^2

Simple...Thanks a lot for your help!
 

1. What is projectile motion?

Projectile motion is the motion of an object through the air due to the force of gravity. It follows a curved path known as a parabola.

2. How does a grasshopper move through the air when jumping off a cliff?

A grasshopper jumping off a cliff experiences projectile motion. It is propelled by its muscles and then gravity takes over, causing it to follow a parabolic path until it lands on the ground.

3. What factors affect the projectile motion of a grasshopper off a cliff?

The factors that affect the projectile motion of a grasshopper off a cliff include the initial velocity of the jump, the angle at which it jumps, and the force of gravity.

4. How does the mass of the grasshopper affect its trajectory when jumping off a cliff?

The mass of the grasshopper does not affect its trajectory when jumping off a cliff. According to the law of inertia, the mass of an object does not affect its motion unless acted upon by an external force.

5. Can the trajectory of a grasshopper jumping off a cliff be calculated using equations?

Yes, the trajectory of a grasshopper jumping off a cliff can be calculated using equations such as the projectile motion equations. These equations take into account the initial velocity, angle of projection, and gravitational acceleration to determine the trajectory of the grasshopper.

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