A weight hooked onto the end of a spring fixed to a ceiling bounces up and down. The weight$$s height, h$,$

relative to the ground, in metres, is given by the formula h $=0\mathrm{.}25$ sin$(240$t $90)+1\mathrm{.}5,$ where t is the time, in seconds.

$$

a$)$ Sketch the graph from t $=0$ s to t $=3$ s on the grid provided.  

 b$)$ What is the period of the weight$$s motion? 

 c$)$ Where does weight initially start, relative to its full path of motion?  

 d$)$ Madeline is $1\mathrm{.}5$ m tall and she can reach a farther $0\mathrm{.}3$ m above her head. Is she capable of reaching the weight at its apex $($maximum height$)?$