a body thrown vertically upward returns to the earth in 3sec
what was the initial velocity of the body? what height did the body reach?
neglect the resistance of air.
The answer after solving is 14.7m/s and
11m. please tell me how the answer is arrived.
Vf = Vo + gt,
a. Vo=Vf - gt = 0 - (-9.8)(3/2) = 14.7m/s.
b. h = Vo*t + 0.5gt^2,
h=14.7*1.5 + 0.5*(-9.8)(1.5)^2 =11.03m.
Vf=Vi+at
Om/s=Vi+(9.8m/s²)(3s)
Vi=29.4m/s
d=Vit+(0.5)at²
d=29.4m/s(3s)+(0.5)(3s)²
d=88.2m+44.1m
d=132.3m
To find the initial velocity of the body and the height it reached, we can use the equations of motion for an object under free fall.
1. First, let's find the time it takes for the body to reach its highest point. Since the body is thrown vertically upwards and returns to earth in 3 seconds, we can divide this time in half to find the time it takes to reach the highest point: t/2 = 3 seconds/2 = 1.5 seconds.
2. Next, let's find the acceleration of the body. Since the body is under free fall and neglecting air resistance, the acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.
3. Now, we can use the equation of motion for vertical motion: vf = vi + at, where vf represents the final velocity, vi represents the initial velocity, a represents the acceleration, and t represents the time.
Since the body reaches its highest point and comes to a stop, the final velocity at the highest point is 0 m/s. Thus, we can rewrite the equation as: 0 = vi - 9.8 * (t/2).
Substituting the known values, we get: 0 = vi - 9.8 * 1.5.
4. Solving the equation for the initial velocity (vi): vi = 9.8 * 1.5.
Calculating this, we find: vi = 14.7 m/s.
So, the initial velocity of the body is 14.7 m/s.
5. To find the height the body reached, we will use the equation: h = vi * t + (1/2) * a * t^2.
Since the body reaches its highest point, we know that its final velocity at that point is 0 m/s. Using this, we can rewrite the equation as: 0 = 14.7 * (t/2) + (1/2) * (-9.8) * (t/2)^2.
Substituting the known values, we have: 0 = 14.7 * (1.5/2) + (1/2) * (-9.8) * (1.5/2)^2.
Simplifying this equation, we find: 0 = 11.025 - 1.103125.
Therefore, the height the body reached is approximately 11 meters.
To summarize, the initial velocity of the body is approximately 14.7 m/s, and the height it reached is approximately 11 meters.