1. A projectile is launched at an initial angle of 50o with a speed of vo = 15 m/s from the top of a hill 5 meters above level ground. g) Find the range of the projectile from launch to impact. h) Find the x and y components of the velocity of the projectile as it strikes the ground. i) What is the magnitude of the velocity of the projectile when it strikes the ground? j) Make a sketch of the trajectory labeling the times and positions of the projectile at launch, peak, and impact point.
Solution
x-component of initial velocity, v xi = 15cos50 = 9.6418 m/s
y-component of initial velocity, v y i = 15sin50 = 11.4906 m/s
The final component of x will not change.
so, v xf = 9.6418 m/s
Final component in y-direction
v 2 yf = v 2 yi + 2ad
v 2 yf = 11.4906 2 - 2(9.8)(-5)
v yf = 15.1668 m/s
Magnitude of final velocity v = sqrt ( 9.6418 2 + 15.1668 2 )
v = 17.972 m/s
Total time in the air
t = -15.1668 - 11.4906 / -9.8
t = 2.72 sec
Range , x = v xi t = 26.22 m
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1- A projectile is launched at an initial angle of 50o with a speed of.docx
1. 1. A projectile is launched at an initial angle of 50o with a speed of vo = 15 m/s from the top of a
hill 5 meters above level ground. g) Find the range of the projectile from launch to impact. h)
Find the x and y components of the velocity of the projectile as it strikes the ground. i) What is
the magnitude of the velocity of the projectile when it strikes the ground? j) Make a sketch of the
trajectory labeling the times and positions of the projectile at launch, peak, and impact point.
Solution
x-component of initial velocity, v xi = 15cos50 = 9.6418 m/s
y-component of initial velocity, v y i = 15sin50 = 11.4906 m/s
The final component of x will not change.
so, v xf = 9.6418 m/s
Final component in y-direction
v 2
yf = v 2
yi + 2ad
v 2
yf = 11.4906 2
- 2(9.8)(-5)
v yf = 15.1668 m/s
Magnitude of final velocity v = sqrt ( 9.6418 2
+ 15.1668 2
)
v = 17.972 m/s
Total time in the air
t = -15.1668 - 11.4906 / -9.8
t = 2.72 sec
Range , x = v xi t = 26.22 m
