Question

a ball is projected from a certain point on the surface of a planet at a certain angle with the horizontal surface. The horizontal and vertical displacement x and y vary with time t in seconds as,x= 10√(3t) and y=10-t^2. Maximum height attained by the ball?
1. 100m
2. 75m
3. 50m
4. 25m

Answer 1

Answer on Question #48741 – Physics – Mechanics | Kinematics | Dynamics

1. A ball is projected from a certain point on the surface of a planet at a certain angle with the horizontal surface. The horizontal and vertical displacement $x$ and $y$ vary with time $t$ in seconds as $x = 10\sqrt{3t}$ and $y = 10 - t^2$. Maximum height attained by the ball?

1. $100\mathrm{m}$

2. $75\mathrm{m}$

3. $50\mathrm{m}$

4. $25\mathrm{m}$

Now we can find the maximum of the function $y(x) = 10 - \frac{x^4}{90000}$.

As the function $y(x)$ is quadratic, the maximum value of the ordinate is

$$y_{\max} = y(0) = 10 - \frac{0^4}{90000} = 10 \, (\mathrm{m}).$$

Answer: $10\mathrm{m}$

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