A man jumps straight up at 5m/s.
a. Determine the time the man is in the air.
b. Determine the maximum height the man would reach.
c. As he jumps, a jerk pushes him in the back, giving him a velocity of 12m/s. determine the range of the man.
d. Solve for the resultant velocity that the man would have.
To determine the answers to your questions, we need to use some basic physics equations. Let's break it down step by step:
a. To determine the time the man is in the air, we can use the equation for vertical motion:
Δy = v0 * t + (1/2) * a * t^2
In this case, the initial velocity (v0) is 5 m/s, the acceleration (a) due to gravity is -9.8 m/s^2 (taking downward as negative), and Δy is the height the man reaches.
Since the man jumps straight up and reaches a maximum height, Δy is equal to zero. By substituting the given values into the equation, we get:
0 = 5 * t + (1/2) * (-9.8) * t^2
Rearranging the equation leads to a quadratic equation:
-4.9t^2 + 5t = 0
Factoring out t from this equation gives us two solutions: t = 0 and t = 1 second.
The time the man is in the air is 1 second.
b. To determine the maximum height the man reaches, we can use the equation for vertical motion:
Δy = v0 * t + (1/2) * a * t^2
Here, Δy represents the maximum height. By substituting the given values into the equation, we have:
Δy = 5 * 1 + (1/2) * (-9.8) * 1^2
Calculating this equation gives us:
Δy = 5 - 4.9
Δy = 0.1 meters
The maximum height the man reaches is 0.1 meters.
c. To determine the range of the man when pushed by a jerk, we need to know the horizontal velocity the man has after being pushed. Since there is no horizontal acceleration, the velocity remains constant at 12 m/s.
The range is the horizontal distance covered by the man. To calculate it, we can use the equation:
Range = velocity * time
Since the time the man is in the air is 1 second (as determined earlier), we can substitute the values:
Range = 12 * 1
Range = 12 meters
The range of the man is 12 meters.
d. To solve for the resultant velocity that the man would have, we need to combine the vertical and horizontal velocities.
The vertical velocity is given as 5 m/s, and the horizontal velocity after being pushed is given as 12 m/s.
The resultant velocity can be calculated using the Pythagorean theorem:
Resultant Velocity = sqrt((Vertical Velocity)^2 + (Horizontal Velocity)^2)
By substituting the given values, we have:
Resultant Velocity = sqrt((5)^2 + (12)^2)
Resultant Velocity = sqrt(25 + 144)
Resultant Velocity = sqrt(169)
Resultant Velocity = 13 m/s
The resultant velocity that the man would have is 13 m/s.