Question

A B-2 Bomber is on a training mission to hit a target placed in the White Sands Missile Range to test a new bomb design. The B-2 takes off from Lackland Air Force Base in San Antonio Texas heading west towards White Sands New Mexico. The bomb weighs 1.5 tons and is set to detonate when it contacts the ground. The B-2 Bomber will release the bomb flying at 700 mph at 45,000 ft. Earth’s gravity is -32.2 ft/s/s.Using the Kinematic equations below, calculate how many miles out from the target the bomber must be when it releases the bomb to successfully hit the target.

Answer 1

To hit the target, the B-2 bomber must be approximately 1.01 miles out when it releases the bomb.

Step-by-step explanation:

To determine how many miles out from the target the bomber must be when it releases the bomb, we can use the kinematic equations. The equation we need to use is:

vf^2 = vi^2 + 2ad

Where:

vf = final velocity (0 mph)

vi = initial velocity (700 mph)

a = acceleration (-32.2 ft/s/s)

d = distance

Rearranging the equation and converting the units:

d = (vf^2 - vi^2) / (2a)

Plugging in the values:

d = (0^2 - 700^2) / (2 * -32.2)

d = 342775 / -64.4

d ≈ -5327

The negative sign indicates that the distance is in the opposite direction of the bomber's initial velocity. To convert the distance to miles, we need to divide by 5280 (the number of feet in a mile):

d ≈ -5327 / 5280

d ≈ -1.01 miles

Therefore, the bomber must be approximately 1.01 miles out from the target when it releases the bomb to successfully hit the target.