A projectile is fired straight up at a speed of 15 m/s.
How long does it take to reach the top of its motion? The acceleration of gravity is 9.8 m/s2 .
Vf = Vo + gt,
t = (Vf - Vo) / g,
t = (0 - 15) / -9.8 = 1.53s.
To find the time it takes for the projectile to reach the top of its motion, we need to use the equation of motion:
Final velocity (v) = Initial velocity (u) + (acceleration (a) * time (t))
In this case, the initial velocity (u) is 15 m/s and the final velocity (v) is 0 m/s at the top of the motion. The acceleration (a) is -9.8 m/s^2 (negative sign because gravity is pulling the projectile downward).
So, let's plug in the values in the equation:
0 m/s = 15 m/s - (9.8 m/s^2 * t)
Now, let's solve for time (t):
9.8 m/s^2 * t = 15 m/s
t = 15 m/s / 9.8 m/s^2
t ≈ 1.53 seconds
Therefore, it takes approximately 1.53 seconds for the projectile to reach the top of its motion.
To find out how long it takes for the projectile to reach the top of its motion, we can use the concept of projectile motion and the equations of motion.
In this case, the projectile is fired straight up, so the initial velocity (u) is 15 m/s in the upward direction, and the acceleration due to gravity (g) is 9.8 m/s^2 in the downward direction.
The formula we can use to solve for time is the following:
t = (v - u) / g
Where:
t = time taken to reach the top of its motion
v = final velocity at the top of its motion
u = initial velocity (given as 15 m/s)
g = acceleration due to gravity (given as 9.8 m/s^2)
Since the projectile is fired straight up, it will momentarily come to rest at the top of its motion. At this point, its final velocity (v) will be 0 m/s.
Plugging in the given values into the formula, we have:
t = (0 - 15) / 9.8
t = -15 / 9.8
Calculating the value, we have:
t ≈ -1.53 seconds
It is important to note that the negative sign indicates that the time is negative because we are considering the upward direction as positive and the downward direction as negative. However, time cannot be negative in this context. So, we take the absolute value of the time:
|t| ≈ 1.53 seconds
Therefore, it takes approximately 1.53 seconds for the projectile to reach the top of its motion.