Solving Motion Problems Involving a Piñata

[ashvuck101]

Homework Statement

In a new twist on the birthday party game, a piñata hangs from the branch of a very tall tree. Nathan aims and fires a small rock from the ground at an angle θ above the horizontal. He fires it at velocity vo. The rock strikes the piñata just as it reaches the top of it trajectory.

a. Ignoring air resistance, what is the speed with which the rock hits the piñata?
b. Calculate the speed of the rock when it hits the piñata assuming an initial speed of 9.0ms-1 and an angle of 65º with respect to the ground.
c. How high is the piñata?
d. How long will it take the lollies inside the piñata to hit the ground once the piñata breaks?

Homework Equations

er i honestly have no idea how to approach this question i know that u use one of the equations of motion i am assuming

S=ut+1/2at²


it the angle thing that's has got me can someone please push me in the right direction?

The Attempt at a Solution

 

[Chewy0087]

Have you heard of 'resultant speed' ?

You can split a speed in that direction into a 'horizontal speed' & 'vertical speed', using pythagoras, see where you get from there. (Try drawing a right angled triangle)

(Hint: to work out how high the rock will go you're only interested in the vertical)

Edit: And question D? LOL

 

[nlightner]

I would approach this problem by first identifying the known variables and the equations that can be used to solve for the unknowns.

Known variables:
- Initial velocity (vo)
- Angle of launch (θ)
- Acceleration due to gravity (g = 9.8 m/s^2)

Equations that can be used:
- Range equation: R = (vo^2sin2θ)/g
- Maximum height equation: H = (vo^2sin^2θ)/2g
- Time of flight equation: T = 2vo sinθ/g

a. To solve for the speed at which the rock hits the piñata, we can use the range equation. Since the rock hits the piñata at the top of its trajectory, the range (R) will be equal to the height of the piñata. Therefore, we can rewrite the equation as: vo^2sin2θ/g = H. Solving for vo, we get: vo = √(Hg/sin2θ). Plugging in the values of H (height of the piñata) and θ (angle of launch), we can calculate the speed at which the rock hits the piñata.

b. To calculate the speed of the rock at a specific angle and initial speed, we can use the equation for velocity in the x-direction: vx = vo cosθ. Since we are given the initial speed and angle, we can calculate the horizontal velocity (vx) of the rock. Then, using the vertical velocity equation, vy = vo sinθ - gt, we can calculate the vertical velocity (vy) of the rock at the time it hits the piñata. Finally, we can use the Pythagorean theorem to calculate the overall speed of the rock.

c. To find the height of the piñata, we can use the maximum height equation. Plugging in the values of vo and θ, we can calculate the maximum height (H) of the piñata.

d. To calculate the time it takes for the lollies inside the piñata to hit the ground, we can use the time of flight equation. Since the lollies will hit the ground at the same time as the piñata, we can use the same values of vo and θ to calculate the time of flight (T). Then, we can use this time and the acceleration due to gravity