Final answer:
The time for a grasshopper with an initial upward velocity of 2 m/s to reach the highest point in its trajectory is calculated using the change in velocity and acceleration due to gravity. The kinematic equation yields approximately 0.204 seconds, with the closest provided option being 0.2 s.
Step-by-step explanation:
To calculate the time it takes for a grasshopper to reach the highest point in its trajectory, we need to consider the acceleration due to gravity, which is approximately 9.81 m/s² downward. When the grasshopper reaches the highest point, its velocity is momentarily 0 m/s. Using the kinematic equation Δv = a * t, where Δv is the change in velocity, a is acceleration, and t is the time, we can solve for t since we know the grasshopper starts with an initial velocity of 2 m/s upward and the acceleration due to gravity is -9.81 m/s² (negative because it is in the opposite direction of the initial velocity).
Δv = v_final - v_initial
Δv = 0 m/s - 2 m/s = -2 m/s
a = -9.81 m/s²
t = Δv / a = -2 m/s / -9.81 m/s² = 0.204 s
Therefore, the closest time from the options provided is B. 0.2 s, as the result has been rounded to one decimal place.