Question

a ball is thrown upward with an initial horizontal velocity of 8 m/s ,and an initial vertical veocity of 40 m/s

find Vo (V knot)
find the position and velociy of the ball after 2.5 secs
find th and h
find tr and r

Answer 1

A ball is thrown upward with an initial horizontal velocity of $8\,\mathrm{m/s}$, and an initial vertical velocity of $40\,\mathrm{m/s}$

- find Vo (V knot)

- find the position and velocity of the ball after 2.5 secs

- find th and h

- find tr and r

Solution

$$V_0 = \sqrt{V_{0y}^2 + V_{0x}^2} = \sqrt{40^2 + 8^2} = 40.8\,\frac{\mathrm{m}}{\mathrm{s}}$$ $$h(t) = V_{0y}t - \frac{gt^2}{2}$$ $$r(t) = V_{0x}t$$

for $t = 2.5\,\mathrm{s}$: $h = 40 \cdot 2.5 - 0.5 \cdot 10 \cdot 2.5^2 = 68,75\,\mathrm{m}$

$$r = 8 \cdot 2.5 = 20\,\mathrm{m}$$ $$\begin{aligned} V_y(2.5) &= 40 - 10 \cdot 2.5 = 15\,\frac{\mathrm{m}}{\mathrm{s}}; \, V_x = 8\,\frac{\mathrm{m}}{\mathrm{s}}; \, V = \sqrt{V_y^2 + V_x^2} = \sqrt{15^2 + 8^2} \\ &= 17\,\frac{\mathrm{m}}{\mathrm{s}} \end{aligned}$$ $$h_{\max} = 80\,\mathrm{m}$$ $$r_{\max} = 32\,\mathrm{m}$$