2-d examples questions on homework review – football kick (symmetric/asymmetric) review –...
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2-D Examples
• Questions on Homework
• Review – Football kick (symmetric/asymmetric)
• Review – Football field goal (asymmetric)
• Review – Range equation (symmetric)
• Problem 26 – Plane dropping supplies
• Problem 20 – Romeo and Juliet
• Problem 31 – Projectile from cliff
• Example – High fly ball (simultaneous equations).
Questions on Homework• ??
Example 4 – Football Kick (symmetric)
• Football kicked at 20 m/s and θ = 37– V0x = 20 cos θ, V0y = 20 sin θ
– ax = 0 m/s2 , ay = -9.8 m/s2
– Time to maximum height
– Maximum height
– Velocity at maximum height
– Range to maximum height
– Time to hit ground
– Distance at hit ground
– Velocity at hit ground
Example 5 - Football Kick (asymmetric)
• Football kicked at 20 m/s @ 37° - 1 m high
– Time to hit ground
– Distance to hit ground
– Eliminate non-physical time
Example 6 – Field Goal (asymmetric)
• Will it clear goalposts 3 m high, 30 m from kick?
• Strategy
– Find time to go 30 m in x direction.
– Find how high it is, at that time, in the y direction.
– If height greater than 3 m – Field Goal!
Problem 27 – Plane dropping supplies
• Y equation determines time in air!• Voy = 0 (horizontal flight)
• How far will it travel in x given vo.
• Must drop that far in advance.
Problem 20 - Romeo and Juliet
Problem 20 - Romeo and Juliet
• What do you know?– vy = 0, y = 4.5 m, a = - 9.8 m/s2
• What tools do you have?– y = ½ at2 + voyt + yo
– x = voxt + xo
– vy2 = voy
2 + 2ay
• What can you find?– Find voy =9.39 m/s2
– Then find t = 0.958 s (Xword puzzle!)
• How can you use to find answer?– Given x = 5m, ax = 0
– Know t from above.– vox = vx = x/t = 5.2 m/s.
Problem 31 -Projectile from Cliff
Tennis• At serve, a tennis player aims to hit the ball horizontally. (a) What minimum
speed is required for the ball to clear the 0.9-m-high net about 15.0 m from the server, if the ball is “launched” from a height of 2.5 m? (b) Where will the ball land if it just clears the net, and will it be “good” in the sense that it lands within 7.0 m of the net? (c) How long will it be in the air?
Water fountains
• Equation of Parabola
Range Equation (symmetric)
• X and Y equations– y = ½ gt2 + voyt + yo x = voxt + xo
• Find time when y = 0– 0 = ½ gt2 + voyt
– t = 0, t = 2voy / g
• Then find x– x = voxt = 2voxvoy / g
– x = 2vo2sinΘ cosΘ / g
– x = vo2sin2Θ / g
• Θ = 0 (min), Θ = 90 (min), Θ =45 (max)
• Trade-off between x and y motion
• Only works for symmetric!!
Example - Simultaneous Equations• Sequential problems
– Does the football clear the goal, 3 m high and 30 m from the kick?– Does the high fly clear the fence 10 m high and 95 m from home plate?
• Simultaneous problems– When Babe Ruth hit a homer over the 12 m high right-field fence 95 m
from home plate, roughly what was the minimum speed of the ball when it left the bat? Assume the ball was hit 1.0 m above the ground and its path initially made a 40° angle with the ground.
– 12 m = ½ (-9.8 m/s2) t2 + vo sin(40) t + 1m
– 95 m = vo cos(40) t
– t = 95 m / vo cos(40)
– t = 3.74 s– vo == 33.16 m/s
Problem 26 – Hunter aims at target
• Fired horizontal – How much will miss?
• Fired at angle – What angle?
– X equation to range
– Y equation to zero
– Range equation (symmetric)
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