1) Two soccer players start from rest, 58 m apart. They run directly toward each other, both players accelerating. The first player has an acceleration whose magnitude is 0.50 m/s2. The second player's acceleration has a magnitude of 0.30 m/s2.
(a) How much time passes before they collide?
(b) At the instant they collide, how far has the first player run?
2)A ball is thrown straight upward and rises to a maximum height of 38 m above its launch point. At what height above its launch point has the speed of the ball decreased to one-half of its initial value?
3)From her bedroom window a girl drops a water-filled balloon to the ground, 6.9 m below. If the balloon is released from rest, how long is it in the air?
(a) How much time passes before they collide?
(b) At the instant they collide, how far has the first player run?
2)A ball is thrown straight upward and rises to a maximum height of 38 m above its launch point. At what height above its launch point has the speed of the ball decreased to one-half of its initial value?
3)From her bedroom window a girl drops a water-filled balloon to the ground, 6.9 m below. If the balloon is released from rest, how long is it in the air?
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1) let the distance from the 1st player be x , and by using x = Vot + 1/2at^2 u get :
x = 0 + 1/2 (0.5) t^2 --- (1)
58 - x = 0 + 1/2 (0.3) t^2 --- (2)
add these 2 eqn to find t :
=> 58 = t^2 (0.25 + 0.15)
=> t^2 = 145 => t = 12 s (approx)
hence x = 0.5^2 x 12^2 = 36 m (approx)
b) V = Vo + at
=> V = 0 + 0.5 (12) = 6 m/s
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2) let init speed = Vo , at max h V = 0 , so :
0 = Vo^2 - 2gh => h = Vo^2 / 2g
hence Vo = sqrt (2gh) = 27.3 m/s
half the value = 13.65 m/s
so (13.65)^2 = (27.3)^2 - 2g h2
=> h2 = 28.5 m
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3) 6.9 = 0 + 1/2 g t^2
=> t = 1.2 s
x = 0 + 1/2 (0.5) t^2 --- (1)
58 - x = 0 + 1/2 (0.3) t^2 --- (2)
add these 2 eqn to find t :
=> 58 = t^2 (0.25 + 0.15)
=> t^2 = 145 => t = 12 s (approx)
hence x = 0.5^2 x 12^2 = 36 m (approx)
b) V = Vo + at
=> V = 0 + 0.5 (12) = 6 m/s
***************************************…
2) let init speed = Vo , at max h V = 0 , so :
0 = Vo^2 - 2gh => h = Vo^2 / 2g
hence Vo = sqrt (2gh) = 27.3 m/s
half the value = 13.65 m/s
so (13.65)^2 = (27.3)^2 - 2g h2
=> h2 = 28.5 m
***************************************…
3) 6.9 = 0 + 1/2 g t^2
=> t = 1.2 s