A 74.0kN kN spaceship comes in for a vertical landing. From an initial speed of 1.00 km/s {\rm km/s}, it comes to rest in 2.40min min with uniform acceleration.
What braking force must its rockets provide? Ignore air resistance.
-1km/s / (2.4min * 60s/min)
= -1km/s / 144s
= -1/144 km/s^2 * 1000m/km
= -6.94 m/s^2
f=1.26x10^5 N
To find the braking force that the spaceship's rockets must provide, we need to use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
Let's break down the given information:
- Initial speed (u) = 1.00 km/s
- Final speed (v) = 0 m/s (since the spaceship comes to rest)
- Time taken (t) = 2.40 min = 2.40 ×60 = 144 seconds
First, we need to convert the initial speed from km/s to m/s. Since 1 km = 1000 m and 1 s = 1 s, we multiply the initial speed by 1000 to convert it to m/s.
Initial speed (u) = 1.00 km/s = 1.00 × 1000 m/s = 1000 m/s
Next, we can find the acceleration (a) using the equation:
a = (v - u) / t
Substituting the given values:
a = (0 m/s - 1000 m/s) / 144 s = -1000 m/s / 144 s = -6.94 m/s²
Note: The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, which represents deceleration or slowing down.
Now, we have the acceleration (a). To find the braking force (F), we need to know the mass (m) of the spaceship. However, the mass is not given in the question. Therefore, without knowing the mass, we cannot calculate the braking force using the given information.
Therefore, we need additional information, such as the mass of the spaceship, to calculate the braking force.