Calculate the maximum height a ball of mass 1.2 kilograms will attend if projected vertically upwards with an initial velocity of 17 m/s
time to peak (t) ... 17 m/s / 9.8 m/s^2
average velocity during ascent ... (17 m/s + 0 m/s) / 2
max height = (time to peak) * (average ascent velocity)
Well, let's see. To calculate the maximum height, we can use the equation for projectile motion. But before we get into the serious stuff, let me tell you a joke. Why don't scientists trust atoms? Because they make up everything!
Now, back to your question. In projectile motion, the maximum height is reached when the vertical component of the velocity becomes zero. So, we need to find the time it takes for the ball to reach that point.
We can use the equation: Vf = Vi + at, where Vf is the final velocity, Vi is the initial velocity, a is the acceleration, and t is the time. Since the ball is moving vertically upwards, the acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2.
Now, we rearrange the equation to solve for time: t = (Vf - Vi) / a. Plugging in the values, we have t = (0 - 17) / (-9.8). Solving this gives us t ≈ 1.735 seconds.
Next, we can use this time to find the maximum height using the equation: d = Vit + 0.5at^2, where d is the displacement. Plugging in the values, we get d = 17 * 1.735 + 0.5 * (-9.8) * (1.735)^2. The calculation gives us d ≈ 15.06 meters.
So, the maximum height the ball will reach is approximately 15.06 meters. That's pretty high! Just be sure not to stand directly underneath it. Safety first!
To calculate the maximum height reached by the ball, we can use the equation for the vertical motion of an object in free fall.
The equation we will use is:
Δy = (v₀² - v²) / (2a)
Where:
Δy is the change in height (maximum height in this case),
v₀ is the initial velocity,
v is the final velocity (which is 0 when the ball reaches its maximum height),
a is the acceleration due to gravity (-9.8 m/s²).
Let's substitute the given values into the equation:
Δy = (17² - 0²) / (2 * -9.8)
Calculating this expression, we have:
Δy = (289 - 0) / (-19.6)
Δy = -14.795 m
The negative sign indicates that the ball is traveling in the opposite direction to that of positive y-axis (upwards). So, we need to take the absolute value of the result.
Therefore, the maximum height reached by the ball is approximately 14.795 meters.
To calculate the maximum height reached by the ball, we can use the principle of conservation of energy. The initial kinetic energy of the ball is converted into gravitational potential energy at the maximum height.
The formula for gravitational potential energy is:
Potential Energy = mass * gravity * height
Given:
Mass of the ball (m) = 1.2 kg
Initial velocity (u) = 17 m/s (upwards)
First, we need to find the change in velocity when the ball reaches its maximum height. Since the ball is projected vertically upwards, the final velocity (v) at the maximum height will be zero, as it momentarily comes to rest.
Using the equation:
v^2 = u^2 - 2g(h - h0)
where:
v = final velocity (0 m/s)
u = initial velocity (17 m/s)
g = acceleration due to gravity (9.8 m/s^2)
h = maximum height
h0 = initial height (which is zero)
Rearranging the equation to solve for h:
0 = (17 m/s)^2 - 2 * 9.8 m/s^2 * h
h = (17 m/s)^2 / (2 * 9.8 m/s^2)
h ≈ 14.76 meters
Therefore, the maximum height reached by the ball is approximately 14.76 meters.