A stone is projected vertically upwards with a speed of 30ms from the top of a tower of height 50m. Neglecting air resistance determine the maximum height it reached from the ground.[g=10ms^2]
a stone is projecting vertical upword with a speed of 30/s from the top of the tower of night 50m neglecting air resistance, the terming of the maximum hight to reach from the ground (g=10m/5²)
h = Hi + Vi t - 4.9 t^2
v = Vi - 9.81 t
when is v = 0 ? (the top)
t = 30/9.81 = 3.06 seconds coasting up to a stop
so
h = 50 + 30 (3.06) - 4.9 (3.06)^2
a stone is projecting vertical upward with a speed of 30m/s from the top of the tower of hight 50m neglecting air resistance the terming of the maximum hight to reach from the ground (g=10/5²)
Answer please
Well, let's crunch some numbers here! If the stone was projected vertically upwards from the top of a 50m tower with a speed of 30ms, we can calculate the time it takes to reach the highest point using the formula:
v = u + gt,
where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and t is the time.
Since the stone is projected upwards, the final velocity at its highest point is 0, so we have:
0 = 30 + (-10)t.
By rearranging the equation, we can solve for t:
10t = 30,
t = 3 seconds.
Now that we know it takes 3 seconds for the stone to reach its highest point, we can determine the maximum height it reached using the formula:
s = ut + (1/2)gt^2,
where s is the displacement, u is the initial velocity, g is the acceleration due to gravity, and t is the time.
Plugging in the values, we get:
s = 30(3) + (1/2)(-10)(3)^2,
s = 90 - 45,
s = 45 meters.
So, the maximum height the stone reached from the ground is 45 meters. Just don't let it get too high, or it might come crashing down and give gravity a bad reputation.
To determine the maximum height the stone reaches, we need to consider the stone's motion and calculate the time it takes to reach its peak. Once we know the time taken, we can find the maximum height using the equation of motion.
1. First, let's calculate how long it takes for the stone to reach its peak. We can use the following equation of motion:
vf = vi + gt
where:
vf = final velocity (0 m/s at the peak)
vi = initial velocity (30 m/s)
g = acceleration due to gravity (-10 m/s^2)
t = time taken
Rearranging the equation to solve for t, we get:
t = (vf - vi) / g
Here, vf = 0 m/s, vi = 30 m/s, and g = -10 m/s^2. Plugging in these values, we have:
t = (0 - 30) / -10
t = 3 seconds
Therefore, it takes the stone 3 seconds to reach its peak.
2. Now that we know the time taken to reach the peak, we can calculate the maximum height using the equation of motion:
h = vi * t + (1/2) * g * t^2
where:
h = maximum height
vi = initial velocity (30 m/s)
t = time taken (3 seconds)
g = acceleration due to gravity (-10 m/s^2)
Plugging in the values, we get:
h = 30 * 3 + (1/2) * -10 * (3^2)
h = 90 - 45
h = 45 meters
Therefore, the maximum height the stone reaches from the ground is 45 meters.