Final answer:
Using equations of motion, the rose's speed after 1 second is 10.69 m/s, after 2.5 seconds it is -4.28 m/s (indicating downward motion), and it takes 2.09 seconds to reach the highest point.
Step-by-step explanation:
When Romeo throws a rose with an initial speed of 20.5 m/s upwards to Juliet, we can use the physics of projectile motion to find the answers:
A. Speed of the rose after 1 second
The speed of the rose after 1 second can be calculated using the equation of motion v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration (which is due to gravity and is -9.81 m/s2 as it is in the opposite direction to the motion), and t is the time. So, v = 20.5 m/s + (-9.81 m/s2 * 1 s) = 10.69 m/s. After 1 second, the rose would be slowing down due to gravity and have a speed of 10.69 m/s.
B. Speed of the rose after 2.5 seconds
Similarly, after 2.5 seconds, the speed will be v = 20.5 m/s + (-9.81 m/s2 * 2.5 s) = -4.28 m/s. The negative sign indicates that the rose is now moving downwards.
C. Time to reach the top of its path
To find how long it takes the rose to reach the top of its path, we set the final velocity to 0 m/s and solve for time: 0 = 20.5 m/s + (-9.81 m/s2 * t). This gives us t = 20.5 m/s / 9.81 m/s2 = 2.09 s.