You buy a plastic dart gun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 3.8 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?

The maximum horizontal range of your gun = 35.378 m

Explanation:

By shooting the dart straight up, we can use the equations of motion to evaluate the initial velocity of the dart as it comes out from the gun

u = initial velocity = ?

v = final velocity at maximum height = 0 m/s

g = - 9.8 m/s

t = time taken to reach maximum height = (total time of flight of the dart)/2 = 3.8/2 = 1.9s

v = u + gt

0 = u - (9.8 × 1.9)

u = 18.62 m/s.

To shoot a projectile to obtain maximum range, the angle of shot, θ = 45°

Range of a projectile is given as

R = [u² sin (2θ)]/g = [18.62² (sin (2 × 45°))]/9.8

R = 35.378 m

given data:

determine the horse power (h.p) = ?

force applied to move the box(f) = 10 pounds,

box lifted from a distance         (d) = 3 feet

time taken to lift                         (t) = 10 sec,

the horse power is defined as amount of work required to move a load. the horse power is equal to 550 foot-pound per second

                  1 h.p   = 550 foot-pound/second

it can also be defined as the the load that need to be move a body for certain distance in a certain amount of time.

mathematically,

                      h.p = (force × distance)/ time

                            = (10 × 3)/ 10

                            = 30/10

                            = 3 foot -pound/sec

hence, the horse power is needed to move the box is 3 foot-pound/second

important note: 1 h.p = 550 foot-pound/second = 746 watts

prolly a beacuse the momentuem the car has increases while going down hill