A small metal ball is thrown vertically upwards with an initial speed of 20ms^{1}. 

Assuming that air resistance is negligible, calculate 

i) the time taken by the ball to reach its highest point 

ii) the maximum height reached 

iii) the height, h_{1.5} of the ball 1.5s after it was thrown 

iv)
the speed, v_{4} of the ball 4s after it was thrown. 



If we take upwards to be positive then remember that g will have a
negative value in the
calculations 



i) At maximum height, the speed is zero. 

Therefore we have v = 0, u = 20ms^{1}
and g = 9.8ms^{2} 

Rearranging the equation which defines acceleration, we have 





Therefore, time to reach maximum height = 2.04s 



ii) The average value, v_{a} of the speed of the ball is




so the distance moved, h, in time t is given by 



Therefore the maximum height reached by the ball is h = 20.4m 



iii) We will use the equation: 


however, again remember that in this situation, we have defined upwards as
positive 



Therefore the height of the ball at t = 1.5s is h_{1.5}
= 18.98m 



iv) Here we will use the equation: 


again remembering that in this situation, we have defined upwards as positive 



This answer tells us that 4 seconds after the ball was thrown,
its speed was v_{4} = 19.2ms^{1}


The negative sign tells us that it was moving downwards. 
