Linear Motion III Free Falling Bodies Level : Physics I Teacher : Kim Objectives i) Describe the motion of an object in free fall ii) Distinguish between speed and velocity iii) Describe the motion of an object thrown straight up and allowed to free-fall iv) Determine the velocity and distance fallen at any time after an object is released v) Determine the value of the value of the gravitational acceleration g and understand why its value is always constant Speed vs Velocity Speed only indicates how fast an object is moving and does not reveal anything about direction Velocity describes how fast an object is moving and the direction of its motion Ex) A ball is moving to the right, hits a wall and bounces back in the opposite direction of 5m/s. Its speed at that instant is expressed just as v=5m/s. The velocity is expressed as v= -5m/s or v=5m/s(left) Determining the Signs( +, - ) for Velocity and Acceleration i) When objects are moving to the right + v > 0 if v f > v i, then a 0 if v f < v i, then a 0 ii) When objects are moving to the left + v < 0 if v f > v i, then a 0 if v f < v i, then a 0 * The sign of velocity & acceleration is not determined by an object s position but determined by which direction it is moving towards to 1
*Air resistance is ignored through-out the unit! Free-falling Motion Case-1) Dropped from a certain height + v < 0 v f > v i, and a 0 ; always - For free-falling motion, the acceleration due to gravity is always ( ) - The symbol used for gravitational acceleration is ( ) - The sign for g is always ( ) - The value of g is always ( ) m/s - The three formulas used for free-falling motion can be obtained by a= -g, where g=9.8m/s. (also, d y for height=vertical distance) v f = v i + at v f = v i - gt ------------------- (1) d= v i t + (½)at y= v i t - (½)gt ------------------ () ad= v f v i -gy= v f v i ------------------- (3) Q1) An object is dropped from a certain height. If it takes 3 seconds to hit the ground, how high was the object dropped? What is the velocity of the object when it hits the ground? a) +44.1m, +9.4m/s b) - 44.1m, - 9.4m/s c) +14.7m, +9.4m/s d) -14.7m, - 9.4m/s
v f = v i - gt y= v i t - (½)gt -gy= v f v i Q) A boy drops a rock on top of a building. If it takes 4 seconds to hit the ground, how high is the building and at what velocity will the rock hit the ground? a) +19.6m, +9.m/s b) -19.6m, - 9.m/s c) +78.4m, +39.m/s d) -78.4m, - 39.m/s Q3) If you drop an object from a height of 50 meters, how long would it take for the object to hit the ground? At what velocity will the object hit the ground? a) 10.s, +31.3m/s b) 10.s, -31.3m/s c) 3.19s, +31.3m/s d) 3.19s, - 31.3m/s Q4) A ball is thrown downward with an initial velocity of -1m/s from a height of 16 meters. Find the velocity with which it strikes the ground and time it takes to reach the ground. a) -1.4m/s, 0.96s b) +1.4m/s, 1.54s c) -35.4m/s, 0.96s d) +35.4m/s, 1.54s 3
Case-) Upward and downward motion when object is going up, then v 0, v f v i, and a 0 when object is going down, then v 0 v f v i, and a 0 + * The time is takes for an object to go up = time it take for it to come down * initial velocity = final velocity v f = v i - gt y= v i t - (½)gt -gy= v f v i Q5) An object is thrown up in the air and reaches its maximum height in seconds. What is the initial velocity? How high did the object go up? a) +19.6m/s, +19.6m b) -19.6m/s, -19.6m c) 0m/s, +9.4m/s d) 0m/s, -9.4m/s Q6) An archer points her bow straight upward and fires an arrow with an initial velocity of m/s. What is the maximum height that the arrow will reach? How many seconds will it take the arrow to reach its maximum height? a) +14.7m,.4s b) +4.7m,.4s c) 14.7m, 1.9s d) -14.7m, 1.9s 4
v f = v i - gt y= v i t - (½)gt -gy= v f v i Q7) A stone is thrown vertically upward with velocity 40m/s at the edge of a cliff having a height of 110 meters. The stone misses the cliff and continues downward until it hits the ground below. i) Compute the time it took for the stone to strike the ground below the cliff(=total time in the air). ii) With what velocity does it strike? iii) Find the time during when the stone was at its maximum height to when it hit the ground maximum height(v=0) v i v = -v i y=110m Ans) 10.3(s), -61.3m/s, 6.5(s) 5
v f = v i - gt y= v i t - (½)gt -gy= v f v i Practice Questions 1. If a boy dropped a rock off a high cliff, how fast would it be falling after 5 seconds had elapsed? Ans) -49m/s. If an apple fell from a tree, how long would it take to reach a velocity of -3m/s? Ans) 0.306 (s) 3. A ball dropped from a bridge strikes the water in 5 seconds. Calculate the height of the bridge and the velocity with which it strikes the water. Ans) -1.5m, -49m/s 4. A body falls freely from rest. Find the distance it falls in 3 seconds. Find the velocity after falling 70m. Also, find the time required to reach a velocity of -5m/s. Ans) -44.1m, -37m/s,.55(s) 6
v f = v i - gt y= v i t - (½)gt -gy= v f v i 5. In a football game, the referee tosses a coin up with an intial speed of 6m/s. How high does the coin go above its point of release? What is the total time the coin is in the air before returning to its release point? Ans) 1.84m, 1.(s) 6. A ball thrown vertically upward returns to its starting point in 4 seconds. Find its initial velocity. Ans) 19.6m/s 7. A stone is thrown downward with an initial velocity of -8m/s from a height of 5 meters. Find the velocity with which it strikes the ground and time it takes to reach the ground. Ans) -3.5m/s, 1.58(s) 8. A baseball is thrown straight upward with a velocity of 30m/s. How long will it take to reach the maximum height? How high will it rise? How long will it take to return to the starting point? Ans) 3.06(s), 46m, 6.1(s) 7
v f = v i - gt y= v i t - (½)gt -gy= v f v i 9. A bag is dropped from a balloon that is 300 meters above the ground and rising at 13m/s. For the bag, find the maximum height reached and the time it takes for it to the ground. (remember that we ignore air resistance) v=13m/s balloon! bag! y=300m Ans) 8.6m, 9.6(s) 8