1.8 Integration

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Question 102

The vertical velocity $v$ of a test projectile, in $s−1\text{m s}^{-1}$ , is modelled by the function $\sqrt{t}(21 - t)$ for $\ge 0$ , where $t$ is the time in seconds after launch.

Find, using calculus, the time $t$ at which the projectile reaches its maximum vertical velocity.

[3]

A graph of $v$ against $t$ shows a region $R_1$ bounded by the curve and the $t$ -axis between $t = 0$ and the point where the velocity first returns to zero ( $t = 21$ ). A second region $R_2$ is bounded by the curve, the $t$ -axis, and the vertical line $t = K$ , where $K > 21$ .

Given that the area of $R_1$ is equal to the area of $R_2$ , use calculus to determine the exact value of $K$ .

[4]

The vertical velocity $v$ of a test projectile, in $s−1\text{m s}^{-1}$ , is modelled by the function $\sqrt{t}(21 - t)$ for $\ge 0$ , where $t$ is the time in seconds after launch.

Find, using calculus, the time $t$ at which the projectile reaches its maximum vertical velocity.

[3]

Given that the area of $R_1$ is equal to the area of $R_2$ , use calculus to determine the exact value of $K$ .

1.8 Integration

Question 102

Markscheme

1.8 Integration

Question 102

Markscheme

1.8 Integration

Question 102

1.8 Integration Questions

1.8 Integration

Question 102

1.8 Integration Questions