A projectile is fired straight up at a speed of 13 m/s.
How long does it take to reach the top of its motion? The acceleration due to gravity is 9.8 m/s2 .
To find the time it takes for the projectile to reach the top of its motion, we can use the following formula:
time = (final velocity - initial velocity) / acceleration
In this case, the initial velocity is 13 m/s, the final velocity at the top of the motion is 0 m/s (because the projectile momentarily stops before falling back down), and the acceleration due to gravity is -9.8 m/s^2 (negative because it acts in the opposite direction to the initial velocity).
Plugging in these values into the formula, we get:
time = (0 m/s - 13 m/s) / -9.8 m/s^2
time = -13 m/s / -9.8 m/s^2
Calculating this, we find:
time ≈ 1.33 seconds
Therefore, it takes approximately 1.33 seconds for the projectile to reach the top of its motion.
To find the time it takes for the projectile to reach the top of its motion, we can use the equations of motion.
The initial velocity of the projectile is 13 m/s directed upwards, and the acceleration due to gravity is 9.8 m/s^2 directed downwards.
The equation we can use is:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
At the top of the motion, the velocity of the projectile is 0 since it momentarily comes to rest before falling back down. Therefore, we can rearrange the equation to solve for the time:
0 = 13 - 9.8t
Now, we can solve for t:
9.8t = 13
t = 13 / 9.8
t ≈ 1.33 seconds
So, it takes approximately 1.33 seconds for the projectile to reach the top of its motion.