Answer :
Final answer:
The toy rocket, launched with an initial speed of 35.8 m/s, reaches a maximum height of approximately 65.3 meters before stopping. This height is determined using the equations of motion with the acceleration due to gravity. The final calculation uses the relationship between initial speed, acceleration, and height.
Explanation:
Calculating the Maximum Height of a Toy Rocket
To determine how high a toy rocket rises above the ground when shot straight up with an initial speed of 35.8 m/s, we can use the principles of physics, specifically the equations of motion under constant acceleration due to gravity.
The formula we use to calculate the maximum height (h) reached by the rocket is:
- Identify the known values:
- Initial velocity (u) = 35.8 m/s
- Final velocity (v) at the highest point = 0 m/s (the rocket stops rising at the peak)
- Acceleration due to gravity (g) = -9.81 m/s² (the negative sign indicates that gravity acts downward)
The equation we can use is:
v² = u² + 2ah
Where:
- v = final velocity (0 m/s)
- u = initial velocity (35.8 m/s)
- a = acceleration due to gravity (-9.81 m/s²)
- h = height
Setting the final velocity to zero at the peak height, the equation becomes:
0 = (35.8)² + 2(-9.81)h
Simplifying this expression gives us:
- 0 = 1281.64 - 19.62h
- 19.62h = 1281.64
- h = 1281.64 / 19.62
- h ≈ 65.3 meters
Therefore, the toy rocket rises approximately 65.3 meters above the ground before falling back down.
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