Curved Motion Projectile Motion motion ofan object that is projected into the earth’sgravitational pull.
A projectile will follow the curved path of aparabola, so sometimes it is called parabolicmotion.
Curved motion is produced by a constanthorizontal velocity coupled with an verticalvelocity that is accelerating (due to gravity).
The affects of air resistance are neglected inorder to account for constant horizontalvelocity.
An object is thrown from a height of 44.1 m witha horizontal speed of 35.0 m/s. (It will hit in 3 s.)
Horizontally:
35 m
35 m
35 m
vertically
4.9m
14.7 m
24.5 m
Tips for solving Projectile MotionProblems
•Remember that the curved motion isbecause the object is moving at a constantrate across while it accelerates due togravity!
•The time the object is in the air isindependent of the horizontal velocity!
•How far it falls (or rises) depends upon thevertical components: velocity and theheight!
A man throws a ball off of a tower that is 35.0 mtall with a horizontal velocity of 45.0 m/s. Howfar from the base of the tower will the ball hit?
Vertically:
v0 = 0
a = g =-9.80 m/s2
∆h = -35.0 m
∆t = ?
Horizontally:
vh = 45.0 m/s
∆ d = ?
∆d = vh∆t
∆t =
2∆d
a
=
2(-35.0 m)
-9.80 m/s2
= 2.67 s
= (45.0 m/s)(2.67 s)
= 121 m
Sparky the human cannonball sets his cannon sothat it will launch him with a velocity of 25.0 m/sat an angle of 35.0˚ with the horizontal. Theceiling of the arena is 10.0 m above his launchpoint. How far away should he place his landingnet? Will Sparky need that net (will he clear theceiling?)
25.0 m/s
35.0˚
vh
vv
Horizontally:
vh = (cos 35.0˚)(25.0 m/s)
= 20.5 m/s
Vertically:
vv = (sin 35.0˚)(25.0 m/s)
= 14.3 m/s
Horizontally:
vh = 20.5 m/s
∆d = ?
∆d = v∆t
Vertically:
vo = 14.3 m/s
v = -14.3 m/s
a = g = -9.80 m/s2
∆t = ?
∆t =
vf - vi
a
= -14.3 m/s - 14.3 m/s
-9.80 m/s2
= 2.92 s
= (20.5 m/s)(2.92 s)
= 59.8 m
But does he clear the ceiling?
Vertically Upward:
∆t = .5(2.92 s) = 1.46 s
v0 = 14.3 m/s
v0 = 0
∆d = ?
∆d = v0∆t + .5a∆t2
= (14.3 m/s)(1.46 s)
+ .5(-9.80m/s2)(1.46 s)2
= 10.4 m
To land, he would have to rise 10.4 m, but theceiling is only 10.0 m!
He will not make it!
a = g = -9.80 m/s2
1) A plane flying horizontally at 352 m/s wantsto drop a package so that it lands exactly 1250m horizontally away from the drop point. Atwhat height should the pilot fly in order toaccomplish this?
2) A cannonball is launched with a velocity of 50.0m/s at an angle of 40.0˚ with the horizontal.What is the range (the farthest horizontaldistance) of the cannonball and to what heightwill it rise?
3) A man throws a baseball horizontally off ofthe top of a 45.5 m tower and it lands 89.5 maway from the base of the tower. With whatvelocity did the man throw the ball?
4) A cannonball is fired in such a way that itsrange (the total horizontal distance traveled) is325 m and the maximum height it reaches is65.0 m. What must have been the magnitudeand direction of the cannonball’s velocity at itslaunch?
A projectile if fired at a velocity of 125 m/s @ 35.0˚from the edge of a 125 m cliff. A) How long until ithits at ground level? B) How far from the base ofthe cliff will the projectile hit ground? C) What willbe the impact velocity of the projectile?
A student throws a ball with a velocity of 35.0 m/s@ 65.0˚ at a wall that is 50.0 m high and 59.2 maway from him. Does his throw clear the wall? Ifnot, how high up does hit, and does it hit the wallon the way up or on the way down?