AS Mathematics, Berry J., Fentem R., Francis B., Graham T., Harper Collins 2000, Ex 24. P1 Q6 [Modified]

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AS Mathematics, Berry J., Fentem R., Francis B., Graham T., Harper Collins 2000, Ex 24. P1 Q6 [Modified]

Application of Vectors: Motion  

A rocket was launched at a fireworks display. At time $t$ seconds, the position of the rockets, in metres relative to the launch location (let this be the origin $O$), was $\mathbf{r}=20t\mathbf{i}+\left[ {{(t-4)}^{3}}+64 \right]\mathbf{j}$ where $\mathbf{i}$ and $\mathbf{j}$ are horizontal and vertical unit vectors respectively. The rocket exploded when $t=4$.

(i) 

Write down the height of the rocket when it exploded.

(ii) 

Find the displacement of the rocket from $t=3$ to $t=4$.

(iii) 

Show that the Cartesian equation representing the path of the rocket was $y={{\left( \frac{x}{20}-4 \right)}^{3}}+64$ and sketch the path of the rocket. Hence state the direction of movement of the rocket when it exploded.

Suggested Handwritten and Video Solutions
AS Mathematics, Berry J., Fentem R., Francis B., Graham T., Harper Collins 2000, Ex 24. P1 Q6 [Modified]
AS Mathematics, Berry J., Fentem R., Francis B., Graham T., Harper Collins 2000, Ex 24. P1 Q6 [Modified]
AS Mathematics, Berry J., Fentem R., Francis B., Graham T., Harper Collins 2000, Ex 24. P1 Q6 [Modified]

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Published: 25th March 2022

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