Question

Lanzamos desde el suelo una pelota con un ángulo de 45° y queremos colarla en una cesta que está a 7 m de distancia horizontal y a 3.5 m de altura. Calcular con qué velocidad hay que lanzarla.

Answer 1

v₀ = 11.72 m / s

Step-by-step explanation:

This is a missile launch exercise. Let's write the relations for the final position

x = v₀ₓ t

y =
`v_(oy)` t - ½ g t²

Let's use trigonometry to find the initial velocities

sin 45 = v_{oy} / v₀

cos 45 = v₀ₓ / v₀

v_{oy} = v₀ sin 45

v₀ˣ = v₀ cos45

we substitute

x = v₀ cos 45 t

y = v₀ sin 45 t - ½ g t²

in this equation system we have two unknowns and two equations for which it can be solved, let's substitute the values

7 = v₀ 0.707 t

3.5 = v₀ 0.707 t - ½ 9.8 t²

we clear the time in the first equation and substitute in the second

3.5 = v₀ 0.707 (7 / v₀ 0.707) - 4.9 (7 / v₀ 0.707) 2

3.5 = 7 - 480.345 / v₀²

480.345 / v₀² = 7-3.5

v₀² = 480.345 / 3.5

v₀ = √ 137.24

v₀ = 11.72 m / s