PROJECTILE MOTION CHAPTER 3.5

PROJECTILE MOTION THE MOTION OF OBJECTS THROUGH THE AIR IN TWO DIMENSIONS.

INDEPENDENCE OF VECTOR COMPONENTS HORIZONTAL AND VERTICAL MOTION ANALYZED SEPARATELY

GALILEO FIRST ACCURATELY DESCRIBED PROJECTILE MOTION PREDICTED THAT AN OBJECT PROJECTED HORIZONTALLY WILL REACH THE GROUND IN THE SAME TIME AS AN OBJECT DROPPED VERTICALLY

EQUATIONS FOR PROJECTILE MOTION V Y =V oY + GT X Y = V oY T1/2GT 2 X=V oX T V oX =X/T

PARABOLIC PROJECTILE MOTION IS PARABOLIC

RELATIVE VELOCITY VELOCITY IS ALWAYS RELATIVE TO A FRAME OF REFERENCE. VELOCITY IS DENOTED BY TWO SUBSCRIPTS FIRST ONE REFERS TO THEOBJECT SECOND ONE REFERS TO THE REFERENCE FRAME

Practice problem A movie stun driver on a motorcycle speeds horizontally off a 50.0 m high cliff. How fast must the motorcycle leave the cliff-top if it is to land on level ground below, 90.0 m from the base of the cliff where the cameras are?

solution Draw a diagram of action. Write what you know. Solve for time. T = 3.19 s Calculate initial velocity of x Vx = 28.2 m/s = 101 km/h

Practice problem A foot ball is kicked at an angle of 37 degrees with a velocity of 20.0 m/s. Calculate A. the maximum height B. the time of travel before the football hits the ground C. how far away it hits the ground D. the velocity vector at the maximum height E. the acceleration vector at maximum height Assume the ball leaves the foot at ground level.

solution Draw diagram Deal with the questions one at a time! Calculate Vxo and Vyo Vxo = 16.0 m/s; Vyo = 12.0 m/s Calculate time T = 1.22 s Calculate height Y = 7.35 m

Solution cont. Calculate time of travel. T = 2.45 s Calculate range (x) X = 39.2 m Draw velocity vectors at highest point? Vy = 0 Vx = 16 m/s Draw acceleration vector A = -9.81m/s 2 constant

Practice problem Suppose the football was a punt and left the punter’s foot at a height of 1.00 m above the ground. How far did the football travel before hitting the ground? Hint: set Yo = 0 m and Xo = 0 m

solution Draw diagram Y=Yo + VyoT – 1/2GT m=0 + (12.0m/s)T – (4.90m/s 2 )T 2 Rearrange into standard form (4.90m/s 2 )T 2 - (12.0m/s)T -1.00m=0 Use quadratic equation T=2.53 s or s Why is the second choice not useable?

Solution cont. Calculate x X = 40.5 m

question A boy on a small hill aims his water balloon slingshot horizontally, straight at a second boy hanging rom a tree branch a distance away. A the instant the water balloon is release, the second boy lets go and falls from the tree, hoping to avoid being hit. Was he successful? Why?

question A child sits upright in a wagon which is moving to the right at constant speed. The child extends her hand and throws an apple straight upward while the wagon continues to travel forward at constant speed. If air resistance is neglected, where will the apple land?

question A man in a rowboat is trying to cross a river that flows due west with a strong current. The man starts on the south bank and is trying to reach the north bank directly north from his starting point. What should he do?