A bullet is fired from a rifle that is held 1.70 m above the ground in a horizontal position. The initial speed of the bullet is 1078 m/s. Calculate the time it takes for the bullet to strike the ground.
h = 0.5g*t^2 = 1.70 m.
g = 9.8 m/s^2.
t = ?.
To calculate the time it takes for the bullet to strike the ground, we can use the equation of motion for vertical motion.
The equation for vertical motion is:
h = ut + (1/2)gt^2
Where:
h = height (in this case, 1.70 m)
u = initial velocity in the vertical direction (in this case, 0 m/s)
t = time
g = acceleration due to gravity (approximately 9.8 m/s^2)
Since the bullet is fired horizontally, the initial velocity in the vertical direction is 0 m/s. Therefore, the equation simplifies to:
h = (1/2)gt^2
Rearranging the equation to solve for time, we have:
t^2 = (2h/g)
Plugging in the values for height (h = 1.70 m) and acceleration due to gravity (g = 9.8 m/s^2), we get:
t^2 = (2 * 1.70) / 9.8
Calculating this expression:
t^2 = 0.346938775510204
Taking the square root of both sides to solve for time, we have:
t = √0.346938775510204
Evaluating this expression:
t ≈ 0.588 s
Therefore, it takes approximately 0.588 seconds for the bullet to strike the ground.