A small ball rolls off the top of a stairway horizontally with a velocity of 4.5 ms⁻¹. Each step is 0.2 m high and 0.3 m wide. If g is 10 ms⁻², then the ball will strike the nth step where n is equal to (assume ball strike at the edge of the step).
Select all that apply

Question

A small ball rolls off the top of a stairway horizontally with a velocity of 4.5 ms⁻¹. Each step is 0.2 m high and 0.3 m wide. If g is 10 ms⁻², then the ball will strike the nth step where n is equal to (assume ball strike at the edge of the step).

Select all that apply

G1 Physics · Accepted Answer

For horizontal projection, vertical drop at horizontal distance x is y = gx²/(2u²). The corner of the nth step has x = 0.3n and y = 0.2n. With u = 4.5 m/s and g = 10 m/s²: 0.2n = 10(0.3n)²/[2(4.5)²] = n²/45. Hence n = 9. Therefore option A.