1) A ball is fired at an angle of 34 degrees. It travels 45m horizontally before

Question

1) A ball is fired at an angle of 34 degrees. It travels 45m horizontally before landing on the roof of a 14m building. What is the initial velocity?

2)A ball is fired with a velocity of 200m/s at an angle of 38 degrees off of a 200m cliff. If the surface beneath the cliff is level, where and when does the ball land? What was the maximum height of the ball?

3)A ball is being shot from a cannon that is on the ground. The basket is 100m away and is 10m of the ground. If the cannon can only shoot the ball at 30 degrees, what is the velocity of the cannon? how long did the motion take?

Please explain each

Explanation / Answer

1) x direction

45 = v cos(34) t

t = 45/(v cos(34))

y direction

y = y0 + v0y t + 1/2 a t^2

14 = v*sin(34)*t - 0.5*9.81*t^2

plug in for t

14 = v*sin(34)*(45/(v cos(34))) - 0.5*9.81*(45/(v cos(34)))^2

v=29.73 m/s

2) hits the ground when y = 0

0 = 200 + 200*sin(38)*t - 0.5*9.81*t^2

t=26.63 s

x = 200*cos(38)*26.63=4197 m

max height when vy = 0

vy^2 = v0^2 + 2 a y

y = (200*sin(38))^2/(2*9.81)=772.8 m

3) x direction

100 = v*cos(30) *t

t = 100/(v*cos(30))

y direction

10 = v*sin(30)*t - 0.5*9.81*t^2

plug in for t

10 = v*sin(30)*(100/(v*cos(30))) - 0.5*9.81*(100/(v*cos(30)))^2

v=37.01 m/s

t = 100/(37.01*cos(30))=3.12 s

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