Two balls of mas m = 200 g are thrown from the same location on the ground, at t
ID: 1525311 • Letter: T
Question
Two balls of mas m = 200 g are thrown from the same location on the ground, at the same time, with the same velocity of 20 m/s, one at 37 degree and the other at 53 degree above ground. a. Where does each ball land? Discuss your findings. b. Which ball lands back on the ground first? How much later does the other arrive? c. HOW high does each ball reach? d. What can you determine about the relationship between these two angles? e. Based on the information discovered here, what is the one angle that would provide maximum range?Explanation / Answer
a)
Range = Vo^2 * sin (2*thetha) /g
for projectile thrown at 37 degree:
Range = Vo^2 * sin (2*thetha) /g
Range = 20^2 * sin (2*37) /9.8
Range = 20^2 * sin (74) /9.8
= 39.2 m
for projectile thrown at 53 degree:
Range = Vo^2 * sin (2*thetha) /g
Range = 20^2 * sin (2*53) /9.8
Range = 20^2 * sin (106) /9.8
= 39.2 m
both ball lands 39.2 m from starting point. The range are same
b)
let us calculate time of flight
Time of flight : 2*Vo* sin thetha /g
for projectile thrown at 37 degree:
T = 2*Vo* sin thetha /g
= (2*20*sin 37 ) / 9.8
= 2.46 s
for projectile thrown at 53 degree:
T = 2*Vo* sin thetha /g
= (2*20*sin 53 ) / 9.8
= 3.26 s
The one thrown with 37 degree lands first
more time taken by other = 3.26 s -2.46 s = 0.8 s
c)
maximum height = (Vo * sin thetha)^2 /2g
for projectile thrown at 37 degree:
H = (Vo * sin thetha)^2 /2g
= (20 * sin 37)^2 / (2*9.8)
= 7.4 m
for projectile thrown at 53 degree:
H = (Vo * sin thetha)^2 /2g
= (20 * sin 53)^2 / (2*9.8)
= 13 m
the projectile thrown with 37 degree reaches 7.4 m
the projectile thrown with 53 degree reaches 13 m
d)
Both angles are complementry to each other that is sum of both the angles is 90 degree
e)
for maximum rangle angle should be 45 degree