a baloon is rising at a constant speed of 10m/s. when the balloon is 1400 m above the ground a bullet is fired from a gun at ground level straight up at the balloon with a speed of 200 m/s.
a) does the bullet hit the balloon?
b)if so how high above the ground does it hit the balloon?
c) if not, by how much does the bullet miss the balloon?
yes
To determine if the bullet hits the balloon, we need to compare their paths and the time it takes for each of them to reach the same height.
a) Does the bullet hit the balloon?
First, let's calculate the time it takes for the bullet to reach the height of 1400m. We know that the initial speed of the bullet is 200m/s, and we can use the equation:
Vertical distance = Initial velocity * Time + 0.5 * Acceleration * Time^2
Since the bullet is moving upward, the acceleration is -9.8m/s^2 (due to gravity). Setting the initial height to 0, the equation becomes:
1400 = 200t - 0.5 * 9.8 * t^2
Simplifying, this equation becomes:
4.9t^2 - 200t + 1400 = 0
Solving this quadratic equation will give us the time it takes for the bullet to reach the height of 1400m. If the equation has real roots, the bullet hits the balloon. If not, the bullet misses the balloon.
b) If the bullet hits the balloon, how high above the ground does it hit?
Once we determine that the bullet hits the balloon, we can use the time calculated in part (a) and substitute it back into the equation for vertical distance. This will give us the height at which the bullet hits the balloon.
c) If the bullet does not hit the balloon, by how much does it miss?
If we find that the bullet does not hit the balloon, we can calculate the difference between the height of the balloon (1400m) and the maximum height reached by the bullet. This will give us the amount by which the bullet misses the balloon.
By following these steps and solving the equations, we can find the answers to parts (a), (b), and (c) of the problem.