A rocket is shot up with an initial speed of 45.0 m/s.
How long does it take the rocket to reach it's highest point? How high does the rocket rise above the ground?
An acorn falls from a branch that is 8.00 meters from the ground. How long is it in the air? What is the velocity when it reaches the ground?
How long does it take the rocket to reach it's highest point? How high does the rocket rise above the ground?
An acorn falls from a branch that is 8.00 meters from the ground. How long is it in the air? What is the velocity when it reaches the ground?
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The initial speed of the rocket is 45.0 m/s. At its highest point, the speed will be 0.0 m/s. The acceleration is -10 m/s due to gravity and you want to find the time. Since we are missing displacement, use the Big Five equation: Final velocity equals initial velocity plus acceleration multiplied by time, or Vf=Vi+at. So, 0 = 45 + (-10)(t). -45 = -10t. Therefore, Time=4.5 seconds. As for the second part, if you substitute the unknown Time for displacement, you can use the equation: Vf(squared) = Vi(squared) + 2a(delta x). In this equation, delta x equals the total distance. So, 0(squared) = 45(squared) + 2(-10)(delta x). 0 = 2025 -20x. -2025 = -20x. Therefore, x = 101.25 meters above the ground.
The given variables for the acorn problem are: x = -8.0 m (because it is falling), initial velocity = 0.0 m/s, acceleration = -10 m/s(squared), and Time is the unknown. Since we are leaving out final velocity, use the equation: delta x = Vit + .5at(squared). -8 = 0(t) + .5(-10)t(squared). -8 = -5t(squared), 1.6 = t(squared). Therefore, Time = 1.3 seconds. To find final velocity, it is easiest to use the equation: Vf = Vi + at. So, Vf = 0 + (-10)(1.3). Therefore, final velocity = -13 m/s.
I hope that helps.
The given variables for the acorn problem are: x = -8.0 m (because it is falling), initial velocity = 0.0 m/s, acceleration = -10 m/s(squared), and Time is the unknown. Since we are leaving out final velocity, use the equation: delta x = Vit + .5at(squared). -8 = 0(t) + .5(-10)t(squared). -8 = -5t(squared), 1.6 = t(squared). Therefore, Time = 1.3 seconds. To find final velocity, it is easiest to use the equation: Vf = Vi + at. So, Vf = 0 + (-10)(1.3). Therefore, final velocity = -13 m/s.
I hope that helps.