Final answer:
By calculating the time the frog is in the air using the kinematic equation for vertical motion and multiplying it by the given horizontal velocity, the frog would land approximately 1.34 m from the base of the rock, which does not match any of the given options.
Step-by-step explanation:
To find how far from the base of the rock a frog will land, we can use the kinematics equations for projectile motion. The horizontal distance (range) it covers can be found without considering the vertical motion since the horizontal velocity is constant (as the acceleration in the horizontal direction is zero).
First, we need to find the time the frog is in the air. We do this by considering only the vertical motion. The initial vertical velocity is 0 m/s (since it leaps horizontally), and it's accelerating downwards due to gravity (9.8 m/s²). Using the equation:
h = 1/2 g t²
where h is the height (1.2 m), g is the acceleration due to gravity, and t is the time, we can solve for t:
1.2 m = 1/2 (9.8 m/s²) t²
t = √(2 × 1.2 m / 9.8 m/s²)
t = √(0.2448 s²)
t ≈ 0.495 s
Now we can calculate the range using the constant horizontal velocity of the frog (2.7 m/s):
Range = velocity × time = 2.7 m/s × 0.495 s ≈ 1.34 m
This is not one of the given options, which suggests either the question or the provided choices may contain an error. The correct answer based on the given data would be approximately 1.34 m.