Vertical motion under gravity problems.
Take the acceleration due to gravity ‘g’ to be equal to 9.8 ms-2 and neglect air resistance in each question.
Example questions :
( 1.) A construction worker accidentally knocks a brick from a building so that it falls vertically a distance of 50m to the ground. Calculate : ( a.) the time the brick takes to fall the first 25m
( b.) the time the brick takes to reach the ground
( c.) the speed of the brick as it hits the ground
( 2.) On winning a tennis match the victorious player, Boris, smashed the ball vertically into the air at 30 ms-1
( a.) determine the maximum height reached by the ball
( b.) calculate the time that the ball takes to return to its starting position
( c.) calculate the velocity of the ball 5.0 seconds after being hit by Boris
( d.) determine the acceleration of the ball at its maximum height
( e.) draw an acceleration-time graph of the ball’s motion
( f.) draw a velocity-time graph of the ball’s motion
Numerical Answers to the Example questions :
( 1.) ( a.) t = 2.3 s ( b.) t = 3.2 s ( c.) v = 31.3 ms-1
( 2.) ( a.) d = 45.9 m ( b.) t = 6.12 s ( c.) v = 19 ms-1 down ( d.) a = 9.8 ms-2down( e.) and ( f.) are graphs
Practice questions :
( 1.) A builder working at the MCG knocks a large bolt off a scaffold. The bolt falls 50m vertically towards the ground.
( a.) determine the speed of the bolt 1s, 2s and 3s after9.8 ms-1, 19.6 ms-1, 29.4 ms-1,
( b.) calculate the speed of the bolt after it has fallen 10m, 20m and 30m 14.0 ms-1, 19.8 ms-1, 24.2 ms-1
( 2.) A golf ball is thrown vertically into the air and returns to the thrower’s hand a short time later.
Assuming that ‘up’ is the positive direction sketch the following graphs for the ball’s motion :
( a.) distance-time ( b.) displacement-time ( c.) speed-time ( d.) velocity-time ( e.) acceleration-time
( 3.) A book is knocked of a bench and falls vertically to the floor in a time of 0.4 seconds. Calculate :( a.) its speed as it lands 3.92 ms-1 ( b.) the height from which it fell 0.78 m( c.) the distance it falls in the first 0.2s 0.20 m and ( d.) the distance it falls during the final 0.2 s0.59 m
( 4.) While celebrating her 18th birthday, a girl pops the cork off a bottle of champagne. The cork travels vertically into the air. Being a keen physics student, she notices that the cork takes 4 seconds to return to its starting position.
( a.) How long does the cork take to reach its maximum height?2 s
( b.) What was the maximum height reached by the cork?19.6 m
( c.) How fast was the cork travelling initially?19.6 ms-1
( d.) What was the speed of the cork as it returned to its starting point?19.6 ms-1
( e.) Describe the acceleration of the cork after 1s, 2s and 3s constant at 9.8 ms-2
( 5.) At the start of a football match, the umpire bounces the ball and it reaches a vertical height of 15m
( a.) how long does the ball take to reach its maximum height? 1.75s
( b.) one of the ruckmen is able to leap and reach to a height of 4m with his hand.
How long after the bounce should this ruckman endeavour to make contact with the ball?3.25 s
( 6.) A hot-air balloon is 80m above the ground and travelling vertically downwards at 8ms-1 when one of the passengers accidentally drops a coin over the side. How long after the coin reaches the ground does the balloon touch down?6.7 s