its two questions I need all steps and details Thanks Mr. Stick lives on the pla

Question

its two questions I need all steps and details

Thanks

Mr. Stick lives on the planet Teflon where the force due to gravity is different than that of Earth. Mr. Stick drops a small water balloon off the top of a building (v3=0 m/s). He releases the balloon at a height H=10 m above the surface of Teflon. The balloon hits the ground 1.8 seconds after it is dropped and has a velocity V1 on impact. (Neglect Teflonian air resistance.) What is the acceleration due to gravity on the planet Teflon? Peyton Manning, a football quarterback, is traded from the Denver Broncos to the Teflonian Space Nerds. If he can throw a football at a speed of 29 m/s at a horizontal angle of 30 degrees, how much further and higher does he throw the ball after he moves from Earth to Teflon? A football is kicked across a level field. The ball spends 3 seconds in the air and lands 60 m from the point where it was kicked. (Ignore air resistance.) What is the speed of the ball at the top of its trajectory? What is the maximum height H reached by the ball? What is the y-component of the initial velocity that the football is kicked at? What is the speed at which the football lands on the ground

Explanation / Answer

a)

given inital velocty u = 0

Let acceleration due to gravity = g..

so. a = g

distance = s = 10 m

time = t = 1.8 sec

s = ut + 0.5 * a * t^2

so. 10 = 0 + 0.5 * g * 1.8^2

so acceleatrion g = 6.17284 m/sec2

b)

At earth ..

along y - deirecrtion

vertical velocty = v* sin theeta = 29 * sin 30 = 14.5 m /sec

so height in earth h_e = ( v_y^2 / 2g ) = ( 14.5^2 / ( 2 * 9.8 )) = 10.727041 m

time of flight = 2 * v_y / g = 2 * 14.5 / 9.8 = 2.9592 secs

along x- direction....

speed = vcos 30 = 29 * cos 30 = 25.115 m / sec

so distance travelled in x - dir = 25.115 * time = 25.115 *   2.9592 = 74.3195 m

on teflon...

h_f = ( v_y^2 / 2g ) = ( 14.5^2 / ( 2 *6.17284 )) = 17.03025 m

so he can kick ( 17.03025 - 10.727041 ) = 6.303209 m further hifgher

time of flight = 2 * v_y / g = 2 * 14.5 /6.17284   = 4.698 secs

along x - direction ..

speed = vcos 30 = 29 * cos 30 = 25.115 m / sec

so distance travelled in x - dir = 25.115 * time = 25.115 *   4.698    = 117.99027 m

so he can kick ( 117.99027 - 74.3195 ) = 43.67077 m farther

Part 1 ...

along x - direction,,,..

given time = 3 secs..

distaance = 60 m ..

so speed along x... vx = 60 / 3 = 20 m / sec

at the highest point.. the vertical velocity will be .. so at teh highest point .. speed = v_x = 20 m / sec

part 2 ...

along y - direction..

time take to reack top = 3 / 2 = 1.5 sec

intial velocty = v_y

accelelration = 9.8 m /sec

final velocity = 0

so v_y = 9.8 * 1.5 = 14.7 m / sec

now maximum heigth = ( vy^2 / ( 2 * 9.8 ) ) = 11.025 m

part 3 ... y - component = v_y = 9.8 * 1.5 = 14.7 m / sec

part 4 ...

speed at which it lands = speed at which it was kicked

= sqrt ( vx^2 + vy^2 ) = sqrt ( 14.7 ^2 + 20^2 ) = 24.82116 m / sec

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