# Projectile Motion on Escalators: Ice Cream Dilemma Explained

• Nax
In summary, the question asks if an ice cream cone dropped by a student at the top of a down escalator will land on their 1.8 m tall physics professor's head on the adjacent up escalator. Both escalators have identical angles of 40 degrees with the horizontal and a vertical height of 10 m. Using the Galilean transformation, it is determined that the ice cream will indeed land on the professor's head. The time of impact is approximately 1.24 seconds and the vertical height and relative speed of the ice cream with respect to the head at the time of impact can be found using the equations y0i+vy0it-1/2gt^2 and y0p+vy0pt
Nax

## Homework Statement

You are at the mall on the top step of a down escalator when you lean over laterally to see your 1.8 m tall physics professor on the bottom step of the adjacent up escalator. Unfortunately, the ice cream you hold in your hand falls out of its cone as you lean. The two escalators have identical angles of 40 degrees with the horizontal, a vertical height of 10 m. Will the ice cream land on your professor's head? Explain. If it does land on his head, at what time and at what vertical height does that happen? What is the relative speed of the ice cream with respect to the head at the time of impact?

## Homework Equations

y0i+vy0it-1/2gt^2
y0p+vy0pt

## The Attempt at a Solution

I'm able to find time:

10.0-(0.400)sin(40)(t)-1/2(9.81)t^2=1.80+(0.400)sin(40)(t)
-4.905t^2-0.25115t+10.0 = 0.25115t+1.8
-4.905t^2-0.51423t+8.2 = 0
(-4.905t^2-0.51423t+8.2)*-1 = 0 * -1
4.905t^2+0.51423t-8.2 = 0

t = -b +/1 sqrt ( b^2 - 4 ac) / 2a
t = ((-0.51423 +/- sqrt( (0.51423)^2 - 4(4.905) (-8.2) ) / (4.905)*2
t = (-0.51423 +/- 12.694425)/9.81

(-)

t = -13.20866/9.81
t = -1.35

(+)

t= 12.18019525/9.81
t= 1.24

------

I'm not sure how to find the vertical height and relative speed with respect to the head at the time of impact. Insight would be greatly appreciated, thank you. :)

I know we're supposed to make use of a Galilean transformation, but I'm not sure how...

[STRIKE]the question gave you the information, that both professor, ice-cream with student is on escalator. Its pretty safe to assume they have same horizontal velocity (magnitude). So, the answer is yes it will land on professor's head!...This should give you some insight![/STRIKE]

I guess I overlooked some things

Nax said:
I'm able to find time:

10.0-(0.400)sin(40)(t)-1/2(9.81)t^2=1.80+(0.400)sin(40)(t)
-4.905t^2-0.25115t+10.0 = 0.25115t+1.8
-4.905t^2-0.51423t+8.2 = 0
(-4.905t^2-0.51423t+8.2)*-1 = 0 * -1
4.905t^2+0.51423t-8.2 = 0

what is this value (0.400)?...You haven't mentioned anything about it in your question.

Last edited:

## 1. What is projectile motion on an escalator?

Projectile motion on an escalator is the motion of an object that is launched or thrown on an escalator and follows a curved path due to the combination of its horizontal velocity and the vertical motion of the escalator.

## 2. How does the angle of the escalator affect projectile motion?

The angle of the escalator can affect projectile motion by changing the direction and speed of the object's horizontal velocity. A steeper escalator will result in a greater horizontal velocity and a flatter escalator will result in a smaller horizontal velocity.

## 3. What factors can affect the range of a projectile on an escalator?

The range of a projectile on an escalator can be affected by the initial velocity, launch angle, and the angle of the escalator. Other factors such as air resistance and the mass of the object can also have an impact.

## 4. Can a projectile on an escalator reach its maximum height?

Yes, a projectile on an escalator can reach its maximum height. This occurs when the vertical component of its velocity becomes zero, causing the object to stop moving upwards and begin to fall back down.

## 5. How is the motion of a projectile on an escalator different from a projectile on a flat surface?

The motion of a projectile on an escalator is different from a projectile on a flat surface because on an escalator, the object is constantly accelerating due to the changing angle of the escalator. This results in a curved path instead of a straight line trajectory.

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