Provide an appropriate response.
-What two angles of elevation will enable a projectile to reach a target 17 km downrange on the same level as the gun if the projectile's initial speed is 420 m/sec? Assume there is no wind resistance.
A) $0.03 ^ { \circ }$ and $89.97 ^ { \circ }$
B) $35.41 ^ { \circ }$ and $54.59 ^ { \circ }$
C) $35.41 ^ { \circ }$
D) $70.82 ^ { \circ }$ and $19.18 ^ { \circ }$

Question

Provide an appropriate response.
-What two angles of elevation will enable a projectile to reach a target 17 km downrange on the same level as the gun if the projectile's initial speed is 420 m/sec? Assume there is no wind resistance. 
A) $0.03 ^ { \circ }$ and $89.97 ^ { \circ }$
B) $35.41 ^ { \circ }$ and $54.59 ^ { \circ }$
C) $35.41 ^ { \circ }$
D) $70.82 ^ { \circ }$ and $19.18 ^ { \circ }$

Quizplus · Accepted Answer

We can use the range formula, R = (v^2/g)sin(2θ), where R is the range, v is the initial speed, θ is the angle of elevation, and g is the acceleration due to gravity. We can solve for θ by plugging in the given values for R and v and solving for θ.

R = 17 km = 17000 m
v = 420 m/s
g = 9.8 m/s^2

θ = sin^-1((gR)/(v^2))/2
θ = sin^-1((9.8*17000)/(420^2))/2
θ ≈ 35.41° or 54.59°

Both angles can work because the projectile can follow two arcs: a higher, shorter arc or a lower, longer arc. Both will reach the target at the same time. Therefore, the best choice is B, which includes both angles of elevation.

Provide an Appropriate Response 0.03∘0.03 ^ { \circ }0.03∘ And 89.97∘89.97 ^ { \circ }89.97∘

Provide an Appropriate Response $0.03 ^ { \circ }$ And $89.97 ^ { \circ }$