A ball is thrown down and to the right from the window of a building. The ball i

Question

A ball is thrown down and to the right from the window of a building. The ball is given an initial velocity of 10.0 m/s at an angle of 30.0 degrees below the horizontal. Using the standard x,y Cartesian coordinate system.

a) Find the x-component of the initial velocity (v0)x.

b) Find the y-component of the initial velocity (v0)y.

c) If the vertical distance the balls from the window to the ground is 10.0 meters, find the time-of-flight (t) that the ball is airborne.

d) Calculate the horizontal range R of the projectile.

e) Calculate the ball's final y-velocity at impact vy.

f) Calculate the ball's final speed v at impact.

g) Calculate the clockwise angle between the x-axis and the ball's final velocity at impact.

h) Suppose the ball had a z-component of velocity of 4.85 m/s when released. Calculate the speed the ball would have upon impact with this additional velocity component.

Explanation / Answer

a) Vox = vo*cos(30) = 8.66 m/s

b) Voy = Vo*sin(30) = 5 m/s

c)

let t si the time taken to hit the ground

H = voy*t + 0.5*g*t^2

10 = 5*t + 4.9*t^2

4.9*t^2 +5*t - 10 = 0

solving above equation

we get, t = 1.0067 s

d) R = vox*t = 8.66*1.0067 = 8.718 m

e) vy = voy + g*t = 5 + 9.8*1.0067 = 14.87 m/s

f)
vx = vox = 8.66 m/s

V = sqrt(vx^2+vy^2) = 17.2 m/s

g) theta = tan^-1(vy/vx) = 59.78 degrees

h)

V = sqrt(vx^2+vy^2+vz^2) = sqrt(8.66^2+14.87^2+4.85^2) = 17.878 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.