2. Imagine you are standing in the parking lot of your significant other’s apart

Question

2. Imagine you are standing in the parking lot of your significant other’s apartment late at night and wish to get his or her attention by throwing a pebble at the 3rd story bedroom window. You want to throw the pebble gently enough that it hit the window at the peak of its trajectory. If you are 12 m away from the apartment building and the 3rd floor window is 9.0 m high, and the pebble is released form your hand at a height of 2.0 m, with what velocity should you throw the pebble? Explain your reasoning to get full credit.

Explanation / Answer

Vertical distance travelled to reach 3rd story building is Y = 9-2 = 7 m

Horizontal distance travelled is X = 12 m

but according to the problem

12 = Range/2

Range is R = Vo^2*sin(2*theta)/g

24 = Vo^2*sin(2*theta)/9.8

Vo^2*sin(2*theta) = 235.2

2*Vo*sin(theta)*Vo*cos(theta) = 235.2

Vo*cos(theta) = 235.2/(2*Vo*sin(theta))..........(1)

and also using

Vy^2 = Voy^2- 2*g*h

voy is the vertical component of initial velocity = Vo*sin(theta)

Vy is the vertical component of velocity at maximum height = 0 m/sec

0^2 = Vo^2*sin^2(theta) - (2*9.8*7)

Vo^2*sin^2(theta) = 137.2

Vo*sin(theta) = sqrt(137.2) = 11.7 m/sec............(2)

substituting (2) in (1) we get

Vo*cos(theta) = (235.2)/(2*11.7)

Vo*cos(theta) = 10.05 m/sec....(3)

(2)^2+(3)^2

Vo^2= 11.7^2+10.05^2

Vo = sqrt(11.7^2+10.05^2)

Vo = 15.42 is the initial velocity of the pebble

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.