A projectile is launched from the top of a cliff making an angle theta above the

Question

A projectile is launched from the top of a cliff making an angle theta above the horizontal, with speed V0

-neglect air resistance

1.

a. At which point is the acceleration of projectie the largest?

b. What is the speed of the projectile at its highest point?

c. What is the projectiles total time of flight?

d. What is the horizontal distance d in terms of V0, theta, g, and h?

2. Now suppose the projectile is to be launced at an angle of 35 degrees to the horizontal, from launch, at a vertical distance of 3.30 km and a horizontal distance of 9.40 km.

a. Calculate the initial speed required to satisfy the above conditions

b. Calculatethe time of flight of the projectile using the initial speed from part a.

3. Suppose the inital velocity of the projectile in the previous problem were changed so that the horizontal component was half as big, but the vertical component was unchanged. What can ou say about the time it takes to hit the ground at the ase of the cliff. Justify your answer.

Give all the answers in terms of v0, theta, g, h, and d unless values are provided. . At which point is the acceleration of projectile the largest? What is the speed of the projectile at point B? What is the projectile's total time of flight?

Explanation / Answer

a) same at all points

b) v = Vo*costheta

c) T = d/Vo*costheta = d/Vx

d) -h = Vy*T - 0.5*g*T^2

-h = (Vy/Vx)*d - gd^2/2Vx^2

-h = tan theta *d - gd^2/(2*Vo^2*cos^theta)

2) -3300 = tan35*9400 - 4.9*9400^2/(Vo^2*cos^35)

Vo = 255.53 m/s

b) T = 2Vy/g =(2*255.53*sin35)/9.8 = 29.9 = 30 s

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