RI 2023 Y5 H2 Phy Promo Sect BC Solution

Raffles Institution Year 5-6 Physics Department 1 2023 Year 5 H2 Physics Promotional Examination Solution Section B 1 (a) xx x x 1 20.0 1.40 14.286 14.3 m s s ut su t − = = = = = *Final answer to 3 s.f. (b) y x tan32.0 u u°= yx 1 tan32.0 14.286 tan32.0 8.9269 8.93 m s uu − = ° = ° = = *Final answer to 3 s.f. (c) Consider vertical motion of the ball from starting point to point of maximum height. ( ) yy 0 8.9269 9.81 8.9269 0.90998 0.910 s9.81 v u at t t = + = +− = = = *Final answer to 3 s.f. (d) (i) vertical velocity when the ball hits the wall: ( )( ) 1 yy 8.9269 9.81 1.40 4.8071 4.81 m sv u at −= + = +− = − = − OR gradient, y 1 y 0 9.81 4. 8071 4.81 m s1.40 0.90998 v v −− = − ⇒= − = −− *Straight line with negative gradient, positive and negative vy *Correct label values vy / t / s 0 1.40 0 8.93 – 4.81 0.910

Raffles Institution Year 5-6 Physics Department 2 (ii) Height of the wall is the area under the graph from 0 st = to 1.40 st = . OR Height of the wall is the difference in the absolute areas from 0 st = to 0.910 st = and 0.910 st = to 1.40 st = . (e) (i) With air resistance, there is now a resultant force in the horizontal direction that causes the horizontal component of the ball’s velocity to decrease continuously / gradually / at a decreasing rate. (ii) Preferred answer (comparing the rate at which vertical component of velocity changes with and without air resistance) : With air resistance, when t he ball is moving upwards towards its highest point, the vertical component of its velocity decreases to zero at a faster rate compared to the rate when there is no air resistance. When the ball is movi ng downwards from its highest point, the vertical component of its velocity increases at a slower rate compared to the rate when there is no air resistance. Al ternative answer (describing the effect of air resistance on the variation of vertical component of velocity): With air resistance, the acceleration in the vertical direction is no longer constant. When the ball is mo ving upwards, the vertical component of its velocity decreases at a decreasing rate. When the ball is moving downwards, the vertical component of its velocity increases at a decreasing rate. Comments (a) (b) (c) • A number of students stated the answer in terms of the initial velocity u. The question stated ‘calculate’ which means numerical answers are expected. • Students should present their worked solutions clearly. Defining equations with appropriate symbols should be stated first before substituting numerical values. For example in part (c), students could have written yyv u at= + first, where subscript y represents the vertical components of the vectorial physical quantities in the equation. (d) (i) • The area under the graph above the horizontal axis is larger than that below the horizontal axis. Thi