Question

A large boulder is ejected vertically upward from a volcano with an initial speed of 39.4 m/s. Air resistance may be ignored.

a. At what time after being ejected is the boulder moving at a speed 20.3 m/s upward? Express your answer in seconds.
b. When is the velocity of the boulder zero? PS - Another way to ask this question would be - how long does it take the boulder to reach max. height after ejection? Express your answer in seconds.

Answer 1

The time when the boulder is moving at 20.3 m/s upward is approximately 1.95 seconds. It takes about 4.02 seconds for the boulder to reach its maximum height, where its velocity becomes zero.

Step-by-step explanation:

Finding the Time at a Given Upward Speed

The question posed is about projectile motion, specifically the upward motion of a boulder ejected from a volcano. To find the time when the boulder is moving at 20.3 m/s upward, we can use the kinematic equation for uniformly accelerated motion:

v = u + at

Where v is the final velocity, u is the initial velocity, a is the acceleration (due to gravity, which is -9.8 m/s2 since it's directed downwards), and t is the time. Rearranging the equation to solve for t, we have:

t = (v - u) / a

Inserting the values:

t = (20.3 m/s - 39.4 m/s) / (-9.8 m/s2)

t = -19.1 m/s / (-9.8 m/s2)

t ≈ 1.95 s

So, after approximately 1.95 seconds, the boulder's speed is 20.3 m/s upward.

Finding the Time to Reach Maximum Height

To determine when the boulder's velocity becomes zero, we can use the same kinematic equation:

t = (0 m/s - 39.4 m/s) / (-9.8 m/s2)

t = -39.4 m/s / (-9.8 m/s2)

t ≈ 4.02 s

This shows that it takes the boulder approximately 4.02 seconds to reach its maximum height.