A tank is moving away from a soldier with a bazooka at a constant velocity of 7.80 m/s. The bazooka fires a missile which accelerates from rest at 23.2 m/s2. The soldier fires the bazooka when the tank is 185 m away.
A. How long is the missile in the air?
B. How far does the missile travel in the air?
C. How far does the tank travel while the missile is in the air?
D. How fast was the missile going when it hit the tank?
To find the answers to these questions, we can use physics equations and principles. Let's solve them one by one:
A. How long is the missile in the air?
We can use the equation of motion to find the time it takes for the missile to reach the tank. The equation we will use is:
s = ut + (1/2)at^2
Where:
s = distance
u = initial velocity
a = acceleration
t = time
In this case, the missile starts from rest, so the initial velocity (u) is 0 m/s. The acceleration (a) is given as 23.2 m/s^2. The distance (s) is 185 m.
Plugging in these values, we get:
185 = 0*t + (1/2)*23.2*t^2
Simplifying the equation:
92.5t^2 = 185
Dividing both sides by 92.5:
t^2 = 2
Taking the square root of both sides, we get:
t = √2
So, the missile is in the air for approximately 1.414 seconds.
B. How far does the missile travel in the air?
To find the distance traveled by the missile, we can use the equation of motion:
s = ut + (1/2)at^2
In this case, the initial velocity (u) is 0 m/s, as the missile starts from rest. The acceleration (a) is given as 23.2 m/s^2. We already know the time (t) to be approximately 1.414 seconds.
Plugging in these values, we get:
s = 0*1.414 + (1/2)*23.2*(1.414)^2
Simplifying the equation:
s = 0 + (1/2)*23.2*2
s = 23.2
So, the missile travels approximately 23.2 meters.
C. How far does the tank travel while the missile is in the air?
The tank is moving away from the soldier at a constant velocity of 7.80 m/s. To find the distance traveled by the tank while the missile is in the air, we can use the formula:
distance = velocity * time
In this case, the velocity is 7.80 m/s and the time is approximately 1.414 seconds (as calculated earlier).
Plugging in these values, we get:
distance = 7.80 * 1.414
distance ≈ 11.026 m
So, the tank travels approximately 11.026 meters while the missile is in the air.
D. How fast was the missile going when it hit the tank?
To find the final velocity of the missile when it hits the tank, we need to use the equation:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, we know the initial velocity (u) is 0 m/s, as the missile starts from rest. The acceleration (a) is given as 23.2 m/s^2. We already calculated the time (t) to be approximately 1.414 seconds.
Plugging in these values, we get:
v = 0 + 23.2*1.414
Simplifying the equation:
v ≈ 32.7688 m/s
So, the missile was going approximately 32.7688 m/s when it hit the tank.