Question

(1 point) A projectile is fired from ground level with an initial speed of 600 m/sec and an angle of elevation of 30 degrees. Use that the acceleration due to gravity is 9.8 m/sec2. (a) The range of the projectile is meters. (b) The maximum height of the projectile is meters. (c) The speed with which the projectile hits the ground is m/sec.

Answer 1

(a) The range of the projectile is 31,813.18 m

(b) The maximum height of the projectile is 4,591.84 m

(c) The speed with which the projectile hits the ground is 670.82 m/s.

Step-by-step explanation:

Given;

initial speed of the projectile, u = 600 m/s

angle of projection, θ = 30⁰

acceleration due to gravity, g = 9.8 m/s²

(a) The range of the projectile in meters;

`R = (u^2sin \ 2\theta)/(g) \\\\R = (600^2 sin(2* 30^0))/(9.8) \\\\R = (600^2 sin (60^0))/(9.8) \\\\R = 31,813.18 \ m`

(b) The maximum height of the projectile in meters;

`H = (u^2 sin^2\theta)/(2g) \\\\H = (600^2 (sin \ 30)^2)/(2* 9.8) \\\\H = (600^2 (0.5)^2)/(19.6) \\\\H = 4,591.84 \ m`

(c) The speed with which the projectile hits the ground is;

`v^2 = u^2 + 2gh\\\\v^2 = 600^2 + (2 * 9.8)(4,591.84)\\\\v^2 = 360,000 + 90,000.064\\\\v = √(450,000.064) \\\\v = 670.82 \ m/s`