Trigonometry question

Question

You throw a ball at an angle of 50º, and with an initial speed of 25 ft. per second. How far does the ball travel?

Answer 1

Gaurav

The range of a projectile (how far the ball travels) = v² sin (2α) / g.

v is the initial speed (ft/s)

α is the angle of elevation (degrees)

g is the acceleration downwards due to gravity ( 32 ft/s/s)

So you can just plug your numbers into this expression to find the range

Mike

Answer 2

draw a right triangle with 25 the hypotenuse and the bottom acute angle is 50 degrees

find the vertical velocity

sin50°=v/25

v=25sin50°

v=25*(0.766)

v=19.15 feet/sec

up +19.15'/s, down -19.15'/s

change in velocity in the vertical direction is final velocity-initial velocity

so, -19.15-19.15=-38.3'/s

change in vertical velocity=acceleration in vertical direction X total time passed

force of gravity=-32'/s²

-38.3=-32*change in time (total time passed)

change in time=-38.3/-32

change in time=1.1968s

how far does the ball travel horizontally ?

cos50°=horizontal distance/25

horizontal distance=25cos50°

hd=25*0.64278

hd=16.0695'/s

horizontal distance*total time passed equals "how far the ball travels"

16.0695'/sec*1.1968s=distance the ball travels

distance the ball travels=19.2319 feet