Question

Dennis the Menace uses his wrist rocket to fire a "BB" up in the air. He uses a 42N force in pulling back the wrist rocket and the BB s fired with an

initial velocity of 60 m/s.
How high is the BB at its highest point? Use the calculated time from the equation with velocity in it to get the time so you can then use the other
equation to get the highest point (distance)

Answer 1

The maximum height reached by the BB fired with an initial velocity of 60 m/s is approximately 0.3 meters. This is calculated using the kinematic equations for projectile motion, taking the acceleration due to gravity as -9.8 m/s^2.

Step-by-step explanation:

To find the maximum height reached by the BB shot up in the air with an initial velocity using a wrist rocket, we can apply the kinematic equations for projectile motion. Since we are interested in the highest point, the final velocity at this point will be 0 m/s because the BB will momentarily come to rest before descending. We set the direction upwards as positive, which means that the acceleration due to gravity (9.8 m/s2) will be negative in our calculations.

The formula to determine the time it takes to reach the highest point is:

• v = u + at

Where v is the final velocity (0 m/s at the top), u is the initial velocity (60 m/s), a is the acceleration due to gravity (-9.8 m/s2), and t is the time. Rearranging the formula and solving for t, we get:

t = (v - u) / a

Substitute the known values:

t = (0 - 60) / (-9.8)

t = 6.12 seconds (approximately)

This is the time taken to reach the maximum height. Now, we can use another kinematic equation to find the maximum height (h):

• h = ut + (1/2)at2

Plugging in the values:

h = (60 m/s)(6.12 s) + (1/2)(-9.8 m/s2)(6.12 s)2

h = 183.6 m - 183.3 m

h = 0.3 m (approximately)

So, the maximum height reached by the BB is around 0.3 meters.