Question

The walkway leading to Everglades Hall is splattered with raw eggs. The mess is

about a distance of 57 m away from the building. You suspect fellow dorm
residents to be responsible for this. Assuming a horizontal throw and a throwing speed of 60 mph you try to identify the floor from which the eggs have be
en thrown.

From what height have the eggs been thrown?

(Start from the basic equations. Clearly state all known quantities. Then show the individual steps of your work. Always show the equation before substituting numbers. Always use units with numbers.)

Answer 1

Horizontal range is given by u²sin 2q/g

The height of projectile launch is given by u²sin²q/2g

R= u²sin 2q/g

57 m= u²sin 2q/g   (According to question)

Now, u=60 mph=0.44704 *60 meter per second   (As 1 mile per hour= 0.44704 meter/second)

u=26.8224 m/s

So,

R=57 m= (26.8224)²sin 2q/(9.8 m/s²)

Sin 2q=57 m *(9.8 m/s²)/ (26.8224)²

Sin 2q=0.7764

2q= sin^-1(0.7764)=50.93⁰

q=25.465⁰

Thus, The height of projectile launch is given by u²sin²q/2g

H= u²sin²q/2g

H=(26.8224)²(sin² (25.465⁰))/2*9.8 m/s²

H=719.44*0.1848/19.6=6.7832 m