Question

He range R and the maximum height H of a projectile fired at an inclination θ to the horizontal with initial speed v0 are given by the formulas​ below, where g≈32.2 feet per second per second is the acceleration due to gravity. Complete parts A and B. R= 2v20sinθcosθ g H= v20sin2θ 2g

Answer 1

A. R=1098.7ft

B. H=274.7ft

Explanation:

"The question is not complete, here is the complete question

The range R and the maximum height H of a projectile fired at an inclination θ to the horizontal with initial speed v0 are given by the formulas​ below, where g≈32.2 feet per second per second is the acceleration due to gravity. Complete parts A and B.

`R=(2v_o^2sin \theta cos \theta)/(g)`

`H=(v_o^2sin^2 \theta)/(2g)`

A. Find the range R if the projectile is fired at an angle 45° to the horizontal with an initial speed of 190 ft per second

B. Find the maximum height H if the projectile is fired at angle 45° to the horizontal with an initial speed of 190 ft per second"

Solution

A. given the expression for Range R

substitute v= 190 ft/sec and ∅=45°

`R=(2(190)^2sin(45) cos(45))/(32.2)\\\\R=(72200*0.7*0.7)/(32.2)\\\\R=(35378)/(32.2) \\\\R=1098.7ft`

B. . given the expression for maximum height

substitute v= 190 ft/sec and ∅=45°

`H=(v_o^2sin^2 \theta)/(2g)\\\\H=(190*190*0.7*0.7)/(2*32.2)\\\\H=(17689)/(64.4)\\\\H=274.7ft`