If a projectile is fired with an initial velocity of v0 meters per second at an angle α above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x = (v0 cos(α))t y = (v0 sin(α))t − 1 2 gt2 where g is the acceleration due to gravity (9.8 m/s2). (Round your answers to the nearest whole number.) (a) If a gun is fired with α = 30° and v0 = 500 m/s. When will the bullet hit the ground?

a) The bullet hits the ground 51.02 s after it was fired.

b) 22,092.3 units

c) 3188.8 units

Explanation:

a) Assuming that the level the bullet was fired from is the ground level.

The bullet hits the ground when y = 0

y = (v₀ sin(α))t − (1/2) gt²

v₀ = 500 m/s

α = 30°

y = 0

0 = (500 sin 30) t - 0.5(9.8)t²

4.9t² - 250t = 0

t(4.9t - 250) = 0

t = 0 s or (4.9t - 250) = 0

The t = 0 s indicates that the bullet was indeed fired from the ground level.

The time it eventually hits the ground back

4.9t = 250

t = 51.02 s

The bullet hits the ground 51.02 s after it was fired.

b) The distance from the firing point that the bullet lands.

x = (v₀ cos(α))t

At this horizontal distance, t = 51.02 s

Substituting the parameters

x = (500 cos 30°) × 51.02

x = 22,092.3 units

c) Maximum height attained by the bullet

Maximum height is given by

H = (u² sin² α)/2g

H = (500² sin² 30°)/(2×9.8)

H = 3188.8 units

Hope this Helps!!!

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.

it was given as a lesson and guide for prayer.