Help please ! been stuck on this for hours.
A model rocket blasts off and moves upward with an acceleration of 13m/s^2 until it reaches a height of 25m , at which point its engine shuts off and it continues its flight in free fall.
1) What is the maximum height attained by the rocket?
2)What is the speed of the rocket just before it hits the ground?
3) What is the total duration of the rocket's flight?
10m/s
To answer these questions, we need to break down the problem into different parts.
1. What is the maximum height attained by the rocket?
To find the maximum height reached by the rocket, we first need to determine how long it takes for the rocket to reach that height. We can use the kinematic equation:
Δy = Vi*t + 0.5*a*t^2
Where:
Δy = change in height (25m)
Vi = initial velocity (unknown)
a = acceleration (13 m/s^2)
t = time (unknown)
Rearranging the equation, we get:
Vi*t + 0.5*a*t^2 - Δy = 0
Substituting the known values, we get:
Vi*t + 0.5*13*t^2 - 25 = 0
Now, we can solve this quadratic equation for t. Once we find t, we can substitute it back into the equation to find the initial velocity (Vi). Finally, we can calculate the maximum height using the equation:
Maximum height = Δy + Vi*t + 0.5*a*t^2
2. What is the speed of the rocket just before it hits the ground?
Once the rocket's engine shuts off, it enters a free fall, and gravity is the only force acting on it. We can use another kinematic equation to find the final velocity (Vf) just before it hits the ground:
Vf = Vi + a*t
where:
Vf = final velocity (unknown)
Vi = initial velocity (obtained from the previous calculations)
a = acceleration due to gravity (-9.8 m/s^2)
t = time taken for the rocket to hit the ground (unknown)
Since the initial velocity (Vi) is in the upward direction and the acceleration due to gravity (a) is downward, we need to consider the direction while solving this equation.
3. What is the total duration of the rocket's flight?
The total duration of the rocket's flight is the sum of the time it takes to reach the maximum height and the time it takes to hit the ground. We can add the time values obtained in the previous calculations to find the total duration.
By following these steps and employing the kinematic equations, we can find the answers to the given questions.