The maximum height reached by the penguin can be calculated using the vertical component of the launch velocity and gravity. However, the total velocity at a specific horizontal distance from the cliff cannot be determined without additional information, as it would require knowledge of the time of flight or the maximum height reached.
To determine the maximum height reached by the penguin above the ground, we first isolate the vertical component of the velocity using the sine function: v_y = v · sin(θ), which gives us v_y = 7 m/s · sin(35°). The formula for maximum height in projectile motion where air resistance is negligible is h = v_y^2 / (2 · g). Plugging in the values we get the maximum height h. For the penguin's total velocity at a horizontal distance of 5 meters from the cliff, as friction is neglected, the horizontal velocity component remains constant.
As the initial vertical velocity component diminishes with height due to gravity, we cannot determine the exact total velocity and direction without time or maximum height data. The landing position, again, relies on the horizontal range formula: R = (v^2 · sin(2θ)) / g, which tells us if the penguin reaches the river.
The student's question is ambiguous regarding the total velocity at 5 meters from the cliff, as there's a typo stating 'direction of the penguin’s TOTAL velocity at a horizontal distance of 5 meters from the edge of the cliff.' This should possibly refer to the state when the penguin is vertically 5 meters above the ground, not horizontally, because the horizontal distance reached isn't solely determined by time elapsed but also by the initial velocity and angle of projection.
Conclusion: Without additional information, we could not determine the penguin's total velocity at a given horizontal distance. If the question meant vertical height above ground, the total velocity could be calculated using kinematics for projectile motion.