Question

Please answer the questions thoroughly. Clearly show equations used and how you will arrange them to find the relationship of the variables mentioned. Also, please don't just say if something will increase or decrease but provide a ratio (ie. if X decreased by 2, Y will decrease by 4).

1A. How would the horizontal range change if the muzzle velocity was doubled? Explain how you know.
1B. How would the horizontal range change if the height from the ground was doubled? Explain how you know.
1C. How would the horizontal range change if the mass of the ball was doubled? Explain how you know.

Answer 1

Vosino Voj ↑ / Vocoso Hmon Vocoso projectie motion Initial Horizontal and bi vertical components of Velocitles are - Vox= Uo coso , Voy = Vo sino from Kinematic equation y = yo t Vogt- & gt When object him ground Do y=0 O=ht (Vo sino) t- / gtrs 0 Horizontal Vonge X= Voxt = Ni Cosolt t From Vy = Voy-gt at maximum height Vy=0 => 0=Usino-gt, => t = rosino/g) from Vy = Voy - 29 (y - Yo) => 0 = (Vo sino) ²-29 (Hmax ahl Hmor = (Uosino) 29

from kinemote equation y = Yot Voyt - 1/2 gt from Maximum height to ground, a Hmax => Voy = 0 and when object hits ground y=0 o=ht (rosino) I gtz =>t2 = 25+ rosino у 1 1 Total time of flight t=t, ttz= rosinot (2h Vo sino Horizontal range X = Voxt X = (Uo cosol (rosino + /2h Vosino I eq gr to If 2h, 2 V2 bino 9 g x= Vo sino Coso v binocoso g ģ

x=2 vo sino coso - Vor 2 sino coso) = Vosinzo from the above If Vo is doubled equotion - Xe Vos in20 Horizontal ronge Increases by a of 14 since a avori to If the height from the Ground is doubled, from the below equation X = No coso) rosinot [2h vosinto g Horizontal Vonge Increases If the mess of the ball is Doubled, Horizontal Vonge does not change le hass is Independent of mass from above equation- Ronge