Question

A bullet is fired from a rifle that is held 4.20 m above the ground in a horizontal position. The initial speed of the bullet is 1010 m/s. There is no error in the velocity value.
a) Find the time it takes for the bullet to strike the ground. Report the answer in seconds with 3 significant figures.

b) Find the horizontal distance traveled by the bullet. Report the answer in meters with 3 significant figures.

Answer 1

Velocity is a vector quantity, given by magnitude and direction. The initial vertically downward velocity of an object moving horizontally, is zero

a) The time it takes the bullet to strike the ground, is approximately 0.856 s

b) The horizontal distance travelled by the bullet is approximately 865 meters

Reason:

Known parameter;

Height of the riffle above ground, h = 4.20 m

Initial speed of the bullet, vₓ = 1010 m/s

a) The time, t, it takes the bullet to strike the ground, is given by the relation;

$t = \sqrt{\dfrac{2 \cdot h}{g} }$

Where;

g = Acceleration due to gravity ≈ 9.81 m/s²

• $\therefore t = \sqrt{\dfrac{2 \times 4.20}{9.81} } \approx 0.856$

The time it takes the bullet to strike the ground, t ≈ 0.856 s

b) The horizontal distance travelled by the bullet, d = vₓ×t

Where;

t = Time of flight = Time it takes the bullet to hit the ground ≈ 0.856 s

Therefore, rounding to 3 significant figures, we have;

• d ≈ 1010 m/s × 0.856 s ≈ 865 m

The horizontal distance travelled by the bullet, d ≈ 865 m

Learn more about the trajectory of falling objects here:

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